Apparatus and method to optimize sailing efficiency

ABSTRACT

This invention provides improvements in the efficiency of a sailing vessel through the use of flaps, hydrofoils, or members on the keel of a sailing vessel. One or more are positioned at the top, or root of the keel of the vessel, which primarily generate a force in the windward direction to provide a counter-leeward drift force. One or more are located at the bottom, or tip of the keel of the vessel, which primarily generate a force in the leeward direction to provide a counter-heeling moment. Among other benefits, operation of these flaps, hydrofoils, or members during sailing increases the vessel&#39;s efficiency, in particular its velocity made good. Further, since they are mounted on one appendage, sailing vessels of a rudder and keel design can be equipped with counter leeward-drift and counter-heeling attributes without the need for additional appendages.

CLAIM OF PRIORITY

This application claims priority to and is a continuation of U.S. patentapplication Ser. No. 15/644,001, filed on Jul. 7, 2017, which in turn isa continuation of U.S. patent application Ser. No. 12/397,056, filed onMar. 3, 2009, now U.S. Pat. No. 9,731,799, issued on Aug. 15, 2017,which in turn is a continuation of U.S. patent application Ser. No.11/716,349, filed on Mar. 9, 2007, now U.S. Pat. No. 7,509,917, issuedMar. 31, 2009, the entire contents of which are hereby incorporated byreference.

FIELD OF THE INVENTION

This invention relates to sailing vessels. In particular this inventionrelates to appendages extending from a sailing vessel hull-keels,centerboards, dagger boards, and the like. More particularly, thisinvention relates to sailing vessel appendages that simultaneouslycontrol leeward drift forces, heeling forces, effective weight, anddrag. Although adaptable to sailing vessels of all types, the inventionis particularly suited for high performance sailing yachts.

BACKGROUND OF THE INVENTION

The time required to reach a windward mark on a passage of a sailingyacht is dependent upon the Velocity Made Good (VMG) which, among otherthings, is greatly influenced by four major factors: the amount ofleeward drift of the vessel, the heeling angle of the vessel, theeffective weight of the vessel, and the drag on the vessel.

Velocity Made Good (VMG) is defined as that component of a sailingvessel's velocity made good toward windward. It is that component of avessel's velocity which is directly opposite to the direction of thetrue wind.

The aerodynamic and hydrodynamic fluid forces that act on a sailingvessel as it moves toward its windward mark or destination can beresolved into components that are parallel and perpendicular to thedirection of undisturbed fluid flow. The component parallel to thedirection of undisturbed fluid flow is called a driving force whenacting in a forward direction or drag when opposing forward motion. Thecomponent perpendicular to the direction of undisturbed fluid flow iscalled lift. The lift force of the sails is perpendicular to thedirection of the apparent wind and lift force of the hull is in a planeperpendicular to the course sailed (PPCS).

The leeward drift of a conventional keeled sailing vessel is a result ofthe lateral component of the wind force on the exposed surface areaabove the waterline (including sails, rigging, and hull) and the lateralcomponent of the water forces acting on the surfaces below thewaterline, including the hull, keel, and rudder. In order for a vesselto sail toward its windward mark, the keel and rudder must provideresistance to the leeward drift forces. Since a conventional keel issymmetrical, this can only be accomplished by establishing a leewardangle of attack which makes the vessel angle, or crab, toward itsobjective. The leeward angle λ is defined as the angle between thecourse steered and the course, or track, sailed.

The minimum resistance offered by the water to forward motion of thecanoe body and keel of a sailing vessel occurs when the vessel ispointed directly opposite to the incident fluid flow, that is, in thedirection of the course sailed. Therefore, directing a vessel at aleeward angle to its track through the water increases the drag on itshull and keel. The increased drag reduces the forward velocity of thevessel. The decrease in the forward velocity, in turn, reduces thevelocity made good, VMG.

The heeling angle of a sailing vessel is proportional to the lateralforces of the wind pressing upon its sails, rigging and hull as well aslateral water forces on its hull, keel and rudder. When a vessel issailing upright, or perpendicular to the plane of the surface of thewater, it captures the maximum available wind and therefore has themaximum amount of wind energy to convert into forward propelling energy.When a sailing vessel is heeling, the horizontal projection of the sailarea is reduced in proportion to the increase in heeling angle. Thus,forward propelling energy is lost because less wind energy is capturedby the sails. Unfortunately, what suffers most when the sails areinclined is the production of the upper areas of the sails since theyare brought closer to the water surface where, due to wind shear, thewind velocity is lower. It is not uncommon for the wind velocity at deckaltitude to be 25% less than velocity at the top of a 45 foot mast.Since the wind force is proportional to the square of the velocity, thistranslates to about a 43% reduction in wind force. Therefore, as a boatheels, the sails are withdrawn from the location where the wind force issignificantly greater.

The aerodynamic and hydrodynamic forces that act on a sailing vessel canbe considered to be perpendicular to the surfaces that generate them.When a vessel is sailing erect, therefore, the total sail forces aremost effective because they are directed within the horizontal plane oftravel. However, when a vessel heels, the total sail force is no longerdirected in the horizontal plane of travel but is angled down by adegree equal to the heeling angle. Thus, the forward propellingforce—that component of the total sail force that is parallel to theincident water flow and thus acts to drive a sailing vessel in thedirection of travel—is also reduced.

The heeling angle also creates a vertical component of the wind forcethat, like gravitational weight such as ballast, acts in a downwarddirection. This downward component of the force is lost to forwardpropelling energy and without compensation would also contribute to theeffective weight of the vessel and thereby increase the displacement,wetted surface, and associated drag. The lift force generated by thesymmetrical keel of a conventional sailing vessel is in a planeperpendicular to the course sailed, PPCS, and is a function of the angleof attack of the keel to the incident water. Therefore when the helmcompensates for an increased leeward drift force by increasing theleeward angle, the angle of attack of the keel is increased. Theincreased lift force so produced comprises a horizontal component thatcounters the leeward drift force of the sails and an upward verticalforce component that counters the downward force exerted by the sails,thus returning the vessel to equilibrium and maintaining its originaltrack. This is not without cost, however, because the higher angle ofattack increases the induced drag on the vessel.

Other losses are introduced by heeling because the shape of the hull isusually optimized for minimum drag and/or wetted surface when the vesselis sailing upright or perpendicular to the plane of the water. For thisreason, the drag is also increased by heeling, at an additional expenseto the forward velocity of the vessel.

Further, the horizontal force that the keel provides to resist leewarddrift is a function of the heeling angle of a vessel and, all otherthings being equal, is diminished as the cosine of the heeling anglediminishes with an increase in the heeling angle.

The weight, or more properly, the effective weight of a sailing vessel,at any given moment, determines the displacement and therefore thewetted surface and related drag on a sailing vessel. A decrease in theeffective weight results in a decrease in the wetted surface andassociated drag with an attendant increase in forward velocity. Lesseffective weight also improves the vessel's ability to reach a planingcondition.

As stated above, a decrease in weight or effective weight is accompaniedby a decrease in drag on a sailing vessel. A decrease in the effectiveweight can be achieved by a reduction in the heeling angle which willredirect the force exerted by the sails into a more horizontaldirection. Accordingly, cascading benefits will accrue: a proportionalcomponent of the sail force will be converted from a vertically downwardor effective weight force into forward driving force which increases thevelocity of the vessel; a higher velocity permits a reduction in theleeward angle that must be sailed in order to reach a given mark; thereduced leeward angle decreases the drag associated with the angle ofattack of the keel and the crabbing of the canoe body of the sailingvessel.

The overall efficiency of a sailing vessel can be substantially improvedby a decrease in leeward drift, heeling angle, effective weight, ordrag; provided, of course, that the improvement in any one of thesecharacteristics is not obtained at an equivalent or greater expense ofone or more of the other characteristics.

Early yacht designs incorporated fixed, symmetrical appendages known asconventional keels, which extended down from the hull in alignment withthe vertical longitudinal midplane of the vessel. An essential functionof the keel was to resist leeward drift caused by the lateral componentof wind force on the vessel. This required a vessel to maintain aheading at a leeway angle to the course sailed.

Later designs for sailing vessels have utilized asymmetric hydrofoilsintended to counter the forces that cause leeward drift. Althoughefficient in this regard, the horizontal and vertical components of theforces exerted by these hydrofoils, however, either increased theheeling force, or increased the effective weight.

U.S. Pat. No. 6,032,603 discloses such a prior art, asymmetrichydrofoil, keel design. FIG. 3 of that patent is reproduced as FIG. 1here. The sailing vessel is shown on a starboard tack heeling at anangle of 20 degrees. The hydrofoil is mounted on the keel, with itscambered surface facing toward the windward side, to create a generallywindward directed, counter-leeward drift force. This does give relief tothe leeward drift forces acting on the vessel; that is, the counterleeward-drift force equals the lateral force, Q, generated by thehydrofoil, times the cosine of the heeling angle of the vessel. Thehydrofoil also generates, however, a heeling moment which is equal tothe force, Q, times its perpendicular distance from the line of thatforce to the (instant) axis of rotation of the sailing vessel.

Symmetric keels of traditional sailing vessels oppose leeward drift bysailing at a leeward angle to the track of a vessel but leeward driftcan also be opposed by an asymmetric hydrofoil designed and located toprovide counter-leeward drift forces. The latter is more efficient intwo ways. First, for a given value of counter-leeward drift force, anasymmetric hydrofoil can move at a lower angle of attack therebyinducing less drag and second, since the counter-leeward drift forcegenerated by an asymmetric hydrofoil reduces the required leeward angle,it permits the vessel to point closer to its desired track. It isnoteworthy that although an asymmetric hydrofoil does not requiresailing at a leeward angle to produce a counter leeward drift force asdoes a symmetric keel shape, if necessary it can do so, which wouldincrease its angle of attack and thus its lifting force and, like itssymmetric cousin, but to a lesser extent, its drag will also increase.

FIG. 1 provides an example of an asymmetric hydrofoil mounted on thekeel of a sailing vessel. The hydrofoil has a cambered surface facinggenerally toward the windward side of the vessel and a non-camberedsurface facing generally toward the leeward side of the vessel. Thevelocity over the cambered surface is higher than the velocity over thenon-cambered surface and according to Bernoulli's principal, an increasein velocity will be accompanied by a proportional decrease in pressure.Thus, in this case, differential between the lower pressure on thecambered side and the higher pressure on the non-cambered side of thehydrofoil produces a force Q toward the windward side of the vessel.Then, as shown, its horizontal component serves to oppose leeward driftforces acting on the vessel. It must be noted though, that force Q alsoacts at a perpendicular distance from the instant axis of rotation ofthe vessel and force Q multiplied by this distance exerts a heelingmoment that adds to the existing heeling moments acting on the vessel.

When the wind presses upon the sails of a traditional sailing vessel,the vessel heels and the center of buoyancy moves from the midplane ofthe vessel to leeward. Since the weight and buoyancy forces are then nolonger in vertical alignment, they form a counter-heeling couple,tending to right the vessel. When additional counter-heeling momentswere required, designs called for additional weight or ballast to beadded to the lower end or tip of the keel. Therefore, when a vesselheeled, the ballast acted on the moment arm, so provided, to exert anadditional moment to counter the heeling moments leveraged by the windon the vessel. The amount of ballast that is required to provide anadequate amount of counter-heeling moment can add significantly to theweight of the vessel. Still, such conventional designs afford onlylimited control of the righting moment and the heeling angle can only befurther reduced by lateral motion of the crew or on-board moveableweight.

More recently, a canting keel has been introduced to provide acounter-heeling moment by suspending a ballast bulb beneath the hull ona laterally swinging or canting member that increases the anti-heelinglever arm of the ballast when rotated toward the windward side of atacking sailing vessel. Such mechanisms do resist heeling moments but,like conventional ballast, because they function gravitationally,considerable weight must be incorporated in their design. Additionally,a keel canted to a severe angle can do little to resist leeward driftforces. Therefore, supplementary fore and aft appendages must be addedto provide the necessary counter-leeward drift forces.

A subsequent development in the canting keel is the addition of a hingedhydrofoil or flap mounted on a canting keel or strut that connects thehull to the ballast. This hydrofoil, or flap, is intended to provideadditional heeling resistance when it is necessary to increase theanti-heeling force because the ballast has been canted to its limit andoperating conditions require additional anti-heeling force.

U.S. Pat. No. 5,622,130 discloses such a flap. FIG. 1 of that patent isreproduced as FIG. 2 here. As can be seen, the counter-heeling flap orhydrofoil 20 is mounted on the trailing edge of the keel or strut 14 onan axis along, or parallel to, the longitudinal dimension of the strut14. When activated, unless the keel 14 is vertical, the force generatedby the hydrofoil 20 will be at an angle to the horizontal. Since theflap would only be activated when the vessel was heeling, itshydrodynamic force would be at an angle to the horizontal. Therefore, asthat force acts to resist heeling, it has components that exert both ahorizontal force that increases the leeward drift of the vessel and adownward force that adds to the effective weight of the vessel.Compensation for the increase in these forces can be made by increasingthe leeward angle and thus the angle of attack of the keel.

An example makes this clear. FIG. 3 is a stern view schematic of theprior art shown in FIG. 2 with the appendages 16 and 18 omitted forclarity. As shown in FIG. 3, the flap 20, mounted on a canting keel 14of a sailing vessel, is at an angle of 42 degrees to the verticalbecause the vessel is heeling at an angle (Phi) of 20 degrees, with itskeel canted at an angle (Kappa) of 22 degrees from the midplane of thevessel. When flap 20 is actuated to exert an additional counter-heelingforce (F_(CH)), the horizontal, or drift component of this force(F_(D)), would equal F_(CH)×cosine 42 degrees, or 0.743 F_(CH) acting ina leeward direction, thus increasing the drift of the vessel. Thevertical or weight component of force F_(CH), called F_(W) would equalF_(CH)×sine 42 degrees, or 0.669 F_(CH) acting in a downward direction,increasing the effective weight of the vessel.

Other early designs offer embodiments that were intended to counter theleeward drift forces and the heeling moments with appendages or foilsthat function hydrodynamically. Such foils, however, produce componentsthat exert significant downward forces on the sailing vessel. Theseforces mimic the weight disadvantage of ballast, and tend to pin down orpull the vessel deeper into the water, increasing the displacement, thewetted surface, and the attendant drag, all of which tax the velocity ofthe vessel. In addition, depending upon the attitude, shape orefficiency of the hydrofoil, these forces may create significantadditional heeling moments proportional to the amount of leeway that thevessel is making.

Australian Patent Application AU-A-85 668/82 exemplifies such a design.The embodiment shown in FIG. 3 of that patent is shown here as prior artFIG. 4. As seen in FIG. 4, the vessel is shown heeled 20 degrees on astarboard tack. Two fins, 5 a and 5 b, which are shaped and positionedto produce hydrodynamic forces in a generally downward direction, areshown. The fins are fixed to the tip of the keel and the surfaces ontheir undersides are angled at 20 degrees down from the horizontal whenthe keel is in the vertical position. According to FIG. 4, the force Q′on the windward side, named herein Q′_(W), is equal to the force Q′ onthe leeward side, named herein Q′_(L). If so, the windward fin 5 bproduces no counter-leeward drift lift while the leeward fin 5 aproduces a counter-leeward drift equal to Q′_(L) Sin 40⁰ for a netdecrease in the leeward drift forces acting on the vessel. An additionaladvantage is obtained because the angle of the fins increases theeffective span or draught of the keel as the vessel heels. However, FIG.4 also shows that the vessel must bear the vertically downward oreffective weight forces exerted by both hydrofoils. Together, thesedownward or effective weight forces are the sum of the verticalcomponents of the forces exerted by the hydrofoils, that is: Q′_(W) plusQ′_(L) Cos 40⁰=1.766 Q′.

Still, other prior art keel designs that generate counter-heelingmoments either have no compensation on the keel for the drift forcesthat are necessarily introduced by such counter-heeling designs, oradditional appendages are added elsewhere on the hull to counter thedrift forces. If such compensation is provided by a singlecounter-leeward drift appendage, not in line with the keel, it willlikely establish a yawing moment that can reduce the efficiency of thevessel and compromise the rudder's ability to control the vessel. Twosuch appendages working to compensate for said counter-heeling devicecould be added to the hull to provide counter-leeway drift forces andyawing control but likely would add complexity to the system and drag tothe vessel.

The above-mentioned considerations associated with keels, canting keels,associated hydrofoils and the like apply to the design of any class ofsailing vessel. The need exists for an improved design that reducesheeling, leeward drift, weight, and drag in such a manner that animprovement in one does not significantly degrade another.

This need is particularly acute in the design of high performancesailing yachts specifically designed for the America's Cup Race.Improved designs for America's Cup Class Yachts must conform to thespecifications required by the America's Cup Class Rule Version 5.0

In consideration of designs disclosed herein that are intended toqualify for America's Cup Class Rule Version 5.0, three requirements,which have related significance, are noted. First, Rule 17.10 states:“The maximum number of movable appendages shall be two . . . .” Second,Rule 17.10(a) further limits the movement of these appendages “torotation only.” Third, The Deed of Gift, written in 1887, thatestablished America's Cup Races, contained a few select rules that mustbe followed to this day, including the following: “Center-board orsliding keel vessels shall always be allowed to compete in any race forthis Cup, and no restrictions nor limitations whatever shall be placedupon the use of such center-board or sliding keel, nor shall thecenter-board or sliding keel be considered a part of the vessel for anypurposes of measurement.”

Four formulae of America's Cup Class (ACC) Rule, Version 5.0 that governthe design requirements for sailing vessels competing in The America'sCup are of particular importance. These formulae place interactingrestrictions on the variables: Rated Length in meters (L), MeasuredLength in meters (LM), Displacement in cubic meters (DSP), Rated SailArea in square meters (S), a Weight Penalty, by definition in meters(WP), Weight in kilograms (W), and a Freeboard Penalty in meters (FP).

They are bound in the primary formula of Section B, 5:[L+1.25×(S)⁻²−9.8×(DSP)⁻³]/0.686<=24.000 metrs  (a)and defining formulae, respectively, of Section B, 6.1; Section B, 8.1and Section C, 122:L=LM×[1+2,000×(LM−22.1)⁴]+FP+WP,  (b)DSP=W/1025, where 1,025 kpg/m ³ is the density of sea water  (c)WP=4×[(yacht'sweight in kp)³−28845]  (d)Formula (a) shows that the factors L and/or S can be increased when DSP,which is equivalent to weight, increases. However, formula (d) showsthat for any vessel exceeding 24,000 kilograms a weight penalty (WP) isimposed and according to formula (b) the weight penalty WP will dictateeither a reduction in the measured length LM or an increase in the valueof the rated length L. Referring back to formula (a), if L is increased,S must then be reduced to maintain the formula limit of 24 meters. Itmight be noted that an increase in the weight W also increasesdisplacement DSP but this does little to counteract the disadvantageimposed by the weight penalty WP.

The effect of how a weight change manifests itself on the relativevalues of L and DSP in formula (a) can be shown in the followingexample, wherein the weight of a vessel W=27,000 kilograms:

It is evident from formula (b) that any change in WP is comparable to achange in L. Also, to be on an equal footing in formula (a), a change inL, hence WP, must be compared to a change in the factor “9.8 (DSP)⁻³”.When the weight of the vessel changes, as in this example, from 24,000kgs to 27,000 kgs, the components WP and Δ 9.8 (DSP)³ compare asfollows:

1.  WP = 4[(27,000)⁻³ − (24,000)⁻³] = 4[30 − 28.845] = 4.62  meters$\mspace{76mu}\begin{matrix}{{2.\mspace{20mu}\Delta\mspace{14mu} 9.8\mspace{14mu}({DSP})^{- 3}} = {{9.8\mspace{14mu}\left( {27\text{,}000\text{/}1025} \right)^{- 3}} - {9.8\mspace{14mu}\left( {24\text{.}000\text{/}1025} \right)^{- 3}}}} \\{= {{9.8\mspace{14mu}\left( {2.97 - 2.86} \right)} = {1.08\mspace{14mu}{meters}}}}\end{matrix}$     3.  WP − Δ  9.8  (DSP)⁻³ = 4.62 − 1.08 = 3.54  meters  (11.6  feet)

Therefore, assuming that the Freeboard Penalty (FP) remains unchanged,the Measured Length LM would have to be decreased sufficient to reducethe value of rated length L by 3.54 meters in order to compensate forthe Weight Penalty WP in this example.

It can be seen that, all other things being the same, for a vessel of agiven rated length L and weighing more than 24,000 kg, a decrease in theweight, and therefore a decrease in the weight penalty, (WP), will allowan increase in the measured length (LM) and thus an increase the maximumattainable velocity of such a high performance racing yacht. Analternative would be to not change LM, which would then reduce the valueof the rated Length L. This would then permit an increase in the sailarea. Therefore, it is desirable to enable designers of sailing vesselsin this category to increase counter-heeling moments without addingadditional ballast and without suffering additional drift forces.

Accordingly, the present invention is directed toward overcoming theaforementioned problems associated with keel arrangements and designs,thus creating a more efficient sailing vessel in any class or category.The present invention is further directed toward improved designs,embodiments, and systems that enable the improvement of any one, or anycombination, of the above cited performance characteristics. The presentinvention is still further directed to overcoming the aforementionedproblems associated with keel arrangements and designs while adhering tothe design rules required for boats to participate in the America's CupRace.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a driftcontrol and a heel control system that can simultaneously improveleeward drift, heeling, effective weight and associated drag, or anycombination thereof, to enable an overall improvement in the efficiencyof sailing vessels.

It is a further object of this invention to provide a drift control anda heel control system that enables the selection of any one, or anycombination thereof of the improvements disclosed herein, in order tosatisfy designers' objectives in the creation of efficient sailingvessels in any class or category.

It is an object of this invention to provide designs that incorporateboth counter-leeward drift (CLD) and counter-heeling (CH) flaps orhydrofoils on the keels of sailing vessels.

It is an object of this invention to reduce the drag on a sailingvessel.

It is an object of the present invention to provide an improved sailingvessel keel capable of countering leeward drift forces andsimultaneously countering heeling moments produced by lateral wind andwater forces acting on sailing vessels.

It is a further object of this invention to provide an improved sailingvessel keel that provides counter-leeward drift forces and counter-heelforces while further minimizing the downward forces that increase theeffective weight of the vessel.

It is a further object of this invention to provide an improved keelthat reduces the net leeward drift forces and simultaneously reduces thenet heeling moments produced by lateral forces, with minimal or noincrease in the downward forces that increase the effective weight ofsailing vessels.

It is a further object of the invention to provide a keel capable of notonly eliminating any net downward resulting dynamic forces but alsocapable of yielding a positive or net upward resultant force whileproviding both counter-heeling moments and counter-leeward drift forces.

It is a further object of the invention to provide a keel with acounter-heeling capacity capable of converting some or all of thedownward component of the wind force on the vessel's sails into aresultant increase in forward propelling force with an accompanyingreduction in the vessel's effective weight.

It is a further object of the invention to provide a keel with acounter-heeling capacity not only capable of reducing the heeling angleof a sailing vessel, but also able to effect negative heeling whendesired by the helm to counteract various downward forces acting on asailing vessel.

It is a further object of this invention to provide a keel that canproduce dynamic forces that reduce the required gravitational weightforce of the ballast.

It is an object of the present invention to provide an improved sailingvessel keel capable of countering leeward drift forces with littleincrease or even a decrease in the net heeling moments, downward forces,effective weight forces, drag forces or any combination thereof.

It is an object of the present invention to provide an improved sailingvessel keel capable of countering heeling moments with little increaseor even a decrease in the net leeward drift forces, downward, oreffective weight forces, drag forces or any combination thereof.

It is an object of this invention to provide an improved sailing vesselkeel capable of countering, downward or effective weight forces withlittle increase or even a decrease in the net leeward drift forces,heeling moments, drag forces or any combination thereof.

It is a further object of the present invention to enable the downwardor effective weight to be increased when it is desirable, for example,to reduce pitching or to increase the effective waterline length.

A still further object of the present invention is to provide a keelthat acts hydrodynamically rather than gravitationally in reducing theheeling angle of a sailing vessel thus enabling a reduction or even theelimination of gravitational ballast of a vessel.

It is a further object of the present invention to provide a keel that,while controlling leeward drift forces, acts hydrodynamically andgravitationally in reducing the heeling angle of a sailing vessel thusenabling a reduction in the required gravitational ballast of a vessel.

It is a further object of the present invention to reduce the amount ofballast weight required to counter heeling of a sailing vessel in orderto increase the vessel's potential for hydroplaning and to improve itsdownwind performance without introducing additional leeward driftforces.

It is a further object of the present invention to provide flaps,hydrofoils, or members that counter the heeling moments of a sailingvessel thereby reducing the required ballast and the downward effectiveweight component of the sails, without introducing additional leewarddrift forces, with a resultant reduction in displacement, wetted surfaceof the hull and associated drag.

It is a further object of the present invention to provide flaps,hydrofoils, or members that reduce the heeling angle of a sailingvessel, thereby increasing the forward propelling force component of thesails for an overall improvement in the forward velocity and sailingefficiency of the vessel.

It is also an object of this invention to enable designs that can reducethe heeling moments on a sailing vessel without increasing the leewarddrift forces acting on the vessel.

It is also an object of this invention to enable designs that can reducethe leeward drift forces acting on a sailing vessel without increasingthe downward force or effective weight of a vessel.

It is also an object of this invention to enable designs that can reducethe heeling moment on a sailing vessel without increasing the downwardforces or effective weight of the vessel.

It is also an object of this invention to enable designs that can reducethe weight of a sailing vessel.

It is also an object of this invention to enable designs that can reducethe downward forces or effective weight of a sailing vessel withoutincreasing the leeward drift forces acting on a vessel.

It is also an object of this invention to enable designs that can reducethe downward forces or effective weight of a sailing vessel withoutincreasing the heeling moment of a vessel.

It is also an object of this invention to enable designs that can reducethe downward forces or effective weight of a sailing vessel withoutdecreasing the weight of the vessel.

It is also an object of the invention to provide counter-leeward driftand counter-heeling flaps, hydrofoils, or members each of which performtheir function with a minimum yawing moment on the vessel.

It is an object of the invention to provide counter-leeward drift andcounter-heeling flaps, hydrofoils, or members on a single appendage(e.g. keel) such that sailing vessels of a rudder and keel design areprovided with counter leeward-drift and counter-heeling attributeswithout the need for additional appendages.

It is an object of the invention to have heel control and drift controlsystems that can act independently or interactively, including, but notlimited to any of the following: Systems that can be coupled to yieldoptimum or predetermined sailing characteristics. Systems that can becontrolled by related mechanical, electro-mechanical or like assemblageand/or governed by the helm or in combination with an interrelated, orpredetermined program. Systems that can also incorporate servo controlsto make sensitive, self regulated, automatic performance corrections andsystems that can be controlled in response to positioning, apparent windvelocity and direction, vessel velocity, heading and track data receivedfrom on board instrumentation, GPS or the like and attitude dataobtained from gyroscopic, gravitational, magnetic or likeinstrumentation.

The objects of the present invention will be generally achieved byproviding a sailing yacht with an adjustable hydrodynamic heel controlsystem that acts independent of or in conjunction with, an adjustablehydrodynamic drift control system to simultaneously counter both heeland drift forces.

Further objects of the present invention will generally be achieved byproviding a sailing yacht with a keel-mounted, variable, controllable,counter-leeward drift hydrofoil and a keel-mounted, variable,controllable, counter-heeling hydrofoil.

Still further objects of the present invention will generally beachieved by providing a sailing yacht with a keel-mounted, variable,controllable, counter-leeward drift hydrofoil and a keel-mounted,variable, controllable, counter-heeling hydrofoil that are independentbut can act in conjunction with prior-art drift or heel control systemssuch as fixed ballast or canting keel designs.

Still further objects of the present invention will generally beachieved by providing a sailing yacht with a keel-mounted, singlerotating member that provides primarily counter-leeward drift forces bya hydrofoil-shaped section of the member positioned at an upper andforward facing position on the keel, while simultaneously providingprimarily counter-heeling forces by a second hydrofoil-shaped section ofthe member positioned at a lower and rearward-facing position on thekeel, the entire member acting as one unit but performing two functions.An alternative configuration that will function in essentially the sameway would face the upper, counter-leeward drift hydrofoil toward therear or trailing edge of the keel with the lower, counter-heelinghydrofoil facing toward the forward or leading edge of the keel.

Still further objectives of the present invention will generally beachieved by strategically locating counter-heeling and counter-drifthydrofoils on the vessel that provide dynamic lift to counter both theheeling moments and drift forces.

Further objectives of the present invention will generally be achievedby providing systems and controls that enable variable independent orconnected control of the counter-drift, counter-heel and associatedembodiments disclosed herein.

Further objectives of the present invention will generally be achievedby providing the counter-leeward drift and counter-heeling flaps orhydrofoils closely vertically in line with each other.

Objects of the present invention will be achieved by a sailing vesselhaving a hull, an appendage extending from the hull and having amidplane, a first flap attached to the appendage and rotatable about afirst axis that is disposed within or substantially parallel to themidplane and is also disposed at an angle of less than 90 degrees from avertical plane perpendicular to the midplane, and a second flap attachedto the appendage and rotatable about a second axis that is disposedwithin or substantially parallel to the midplane and is also disposed atan angle of less than 90 degrees from a vertical plane perpendicular tothe midplane.

Further objects will be achieved where at least one of the first axis orthe second axis is substantially parallel to a vertical planeperpendicular to the midplane.

Further objects will be achieved where the first axis and the secondaxis are substantially parallel to a vertical plane perpendicular to themidplane. and substantially vertically aligned.

Further objects will be achieved where at least one of the first axis orthe second axis is adjustable to an angle of less than 90 degrees from avertical plane perpendicular to the midplane.

Further objects will be achieved where at least one of the first flap orthe second flap is attached to the appendage by a hinge.

Further objects will be achieved where one of the first flap or thesecond flap is attached to the appendage at a minimum distance from adesign longitudinal axis of the hull and the other is attached to theappendage at a maximum distance from the design longitudinal axis of thehull.

Further objects will be achieved where the first flap is disposedproximate to the root end of the appendage and extends substantiallytoward the trailing edge of the appendage; and wherein the second flapis disposed at the tip end of the appendage and extends substantiallytoward the trailing edge of the appendage.

Further objects will be achieved where the first flap is disposedproximate to the root end of the appendage and extends substantiallytoward the leading edge of the appendage; and where the second flap isdisposed at the tip end of the appendage and extends substantiallytoward the leading edge of the appendage.

Further objects will be achieved where the first flap is disposedproximate to a root end of the appendage and extends substantiallytoward the leading edge of the appendage; and wherein the second flap isdisposed at a tip end of the appendage and extends substantially towardthe trailing edge of the appendage.

Further objects will be achieved where the first flap is disposedproximate to a root end of the appendage and extends substantiallytoward the trailing edge of the appendage; and where the second flap isdisposed at a tip end of the appendage and extends substantially towardthe leading edge of the appendage.

Objects of the present invention will be achieved by a sailing vesselhaving: a hull; an appendage extending from the hull and having aleading edge, a trailing edge, two surfaces, and a midplane; a firsthydrofoil member, and a second hydrofoil member, and a single, rotatablemember having an axis disposed substantially parallel to the midplane;where the first hydrofoil member and the second hydrofoil member areincorporated in and integral with, the single, rotatable member.

Further objects will be achieved where the first hydrofoil member isdisposed proximate to the root end of the appendage and extends from therotatable member substantially toward the leading edge of the appendage;and where the second hydrofoil member is disposed at the tip end of theappendage and extends from the rotatable member substantially toward thetrailing edge of the appendage.

Further objects will be achieved where the first hydrofoil member isdisposed proximate to the root end of the appendage and extends from therotatable member substantially toward the trailing edge of theappendage; and where the second hydrofoil member is disposed at the tipend of the appendage and extends from the rotatable member substantiallytoward the leading edge of the appendage.

Further objects will be achieved where the first hydrofoil member andthe second hydrofoil member are configured to move toward oppositesurfaces of the appendage when the rotatable member is rotated.

Objects of the present invention will be achieved by a sailing vesselhaving: a hull; an appendage extending from the hull and having aleading edge, a trailing edge, two surfaces, and a midplane; a firsthydrofoil, with at least one cambered side, slidably attached to theappendage; and a second hydrofoil, with at least one cambered side,slidably attached to the appendage.

Further objects will be achieved where the cambered surface of at leastone of the first hydrofoil and the second hydrofoil is disposed at anangle to the midplane of the appendage.

Further objects will be achieved where the first hydrofoil or the secondhydrofoil slide in a track that is substantially parallel to the leadingedge or the trailing edge of the appendage.

Further objects will be achieved where the surfaces flare outward fromthe midplane of the appendage proximate to the root end of the appendagesuch that each hydrofoil may be parked on the flared section when movedto root end of the appendage.

Objects of the present invention will be achieved by a sailing vesselhaving: a hull; an appendage extending from the hull and having aleading edge, a trailing edge, two sides, and a midplane; and aplurality of deformable members; where at least one deformable member isdeposed on each of the two sides.

Further objects will be achieved by including, on each of the two sides:a first deformable member proximate to the root end of the appendage;and a second deformable member proximate to the tip end of theappendage.

Further objects will be achieved by including a first deformable member,disposed on a first side of the appendage and comprising a flexiblesurface; a second deformable member, disposed on a second side of theappendage and comprising a flexible surface; an upper cam configured todeform a portion of the first deformable member at a first rotationalposition and deform a portion of the second deformable member at asecond rotational position; and a lower cam configured to deform aportion of the first deformable member at a first rotational positionand deform a portion of the second deformable member at a secondrotational position.

Objects of the present invention will be achieved by a sailing vesselhaving: a hull having a midplane that includes a design longitudinalaxis of the hull; an appendage extending from the hull and having a rootend, a tip end, and first and second surfaces; a first fixed membermounted on the appendage proximate to the root end and extending fromthe first surface; and a second fixed member mounted on the appendageproximate to the tip end and extending from the second surface.

Further objects will be achieved by including a plurality of theappendages; and a slot, through which at least one of the appendages canbe inserted, where the slot is disposed in a plane at an angle of lessthan 90 degrees from the midplane of the hull.

Further objects will be achieved by including a plurality of theappendages; a slot, adapted to hold at least two appendages; and an axisaround which each appendage pivots; where the axis is disposed within avertical plane and/or a horizontal plane at an angle of 90 degrees orless from the midplane of the hull.

Objects of the present invention will be achieved by a sailing vesselhaving: a hull having a midplane and a design longitudinal axis; anappendage having a root end and a tip end; a first reversible member (1)having a cambered side and a substantially flat side, (2) mounted on theappendage, and (3) having an axis substantially parallel to the designlongitudinal axis of the hull; and a second reversible member (1) havinga cambered side and a substantially flat side, (2) mounted on theappendage, and (3) having an axis substantially parallel to the designlongitudinal axis of the hull; where the first reversible member isdisposed proximate to the root end of the appendage and the secondreversible member is disposed proximate to the tip end of the appendage.

Objects of the present invention will be achieved by a sailing vesselhaving a hull; an appendage extending from the hull; means forgenerating counter-heeling forces; means for generating counter-leewarddrift forces.

Objects of the present invention will be achieved by a sailing vesselhaving: a hull; an appendage extending from the hull; means forhydrodynamically generating counter-heeling forces; means forhydrodynamically generating counter-leeward drift forces.

Further objects will be achieved by including a control system capableof (1) determining apparent wind direction and velocity; (2) determiningthe sailing vessel's position, velocity, heading, track, pitch, yaw, androll; (3) calculating any adjustments necessary to optimize time to adesired mark; (4) adjusting the flaps, hydrofoils, or members tosubstantially achieve the optimization.

Objects of the present invention will be achieved by steps formaximizing the efficiency of a sailing vessel, having a hull, anappendage extending from the hull, a first flap or member attached tothe appendage and a second flap or member attached to the appendage,including: (1) determining a mark; (2) pointing the vessel to a headingnecessary to reach the mark; (3) adjusting a first flap, hydrofoil, ormember attached to the appendage to account for leeward drift forces;and (4) adjusting a second flap, hydrofoil, or member attached to theappendage to account for heeling forces; and (5) readjusting controlsfor optimized sailing efficiency to reach the mark.

Further objects will be achieved where the flaps or members are adjustedby rotating a single unit that is integrally connected to two oppositelyacting flaps or members in order to simultaneously account for leewarddrift and heeling forces.

Objects of the present invention will be achieved by steps formaximizing the efficiency of a sailing vessel, having a hull, anappendage extending from the hull, a first adjustable hydrodynamicmember attached to the appendage, and a second adjustable hydrodynamicmember attached to the appendage, including: (1) determining a mark; (2)determining apparent wind direction and velocity; (3) determining thesailing vessel's position, velocity, heading, track, pitch, yaw, androll; (4) pointing the hull at a heading necessary to reach the mark;(5) adjusting a first hydrodynamic member attached to the appendage toaccount for leeward drift forces; (6) adjusting a second hydrodynamicmember attached to the appendage to account for heeling forces; and (7)readjusting heading for optimized sailing efficiency to reach the mark.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects and advantages of the present invention will becomeapparent from the following description and claims and from theaccompanying drawings, which are not necessarily drawn to scale,especially where necessary to emphasize certain features discussedherein, and wherein:

FIG. 1 is a cross sectional view of a sailing yacht on a starboard tackand heeling at an angle of 20 degrees showing a prior art,counter-leeward drift design, which corresponds to FIG. 3 of U.S. Pat.No. 6,032,603.

FIG. 2 is an isometric view of a sailing yacht showing a prior artcanting keel design, which corresponds to FIG. 1 of U.S. Pat. No.5,622,130.

FIG. 3 is a cross sectional view of the sailing yacht of FIG. 2 above,depicting a prior-art canting-keel design on a starboard tack and withvessel heeling at an angle of 20 degrees and with the keel canted 22degrees from the midplane of the vessel.

FIG. 4 is a cross sectional view of a sailing yacht on a starboard tackand heeling at an angle of 20 degrees, showing a prior-art winged keeldesign, which corresponds to FIG. 3 in Australian Patent ApplicationAU-A-85 668/82.

FIG. 5 is an isometric view of a fixed keel sailing vessel with acounter-leeward drift (CLD) flap and a counter-heeling (CH) flapconstructed in accordance with an embodiment of the present invention.

FIG. 6a is a profile view of an embodiment of the present inventiondepicted in FIG. 5 showing the counter-leeward drift flap 11 above thecounter-heeling flap 12.

FIG. 6b is a detailed profile view of FIG. 6a depicting the keel withtwo vertically hinged flaps.

FIG. 6c is an isometric view of the embodiment shown in FIGS. 6a and 6bproviding additional detail of the hinged flaps depicted in FIGS. 5through 6 b.

FIG. 6d is an isometric view of the embodiment shown in FIGS. 5-6 cdepicting the design longitudinal axis of rotation 10 of the hull and aplane 15 perpendicular to said design longitudinal axis of rotation.

FIG. 6e is a cross-sectional stern view of the vessel shown in FIG. 6dshowing the midplane 6 of the hull, the midplane 16 of the keelappendage, and the design longitudinal axis of rotation 10 of the hull.

FIG. 7a is a cross-sectional, stern view, perpendicular to the coursesailed, PPCS, of a sailing vessel equipped with an upper,counter-leeward drift flap 11 and a lower, counter-heeling flap 12 of anembodiment of the present invention shown in FIGS. 5 through 6 e.

FIG. 7b is a simplified diagram showing the angles and relativedimensions of FIG. 7 a.

FIG. 7c is a graphic representation of the angles and dimensions ofvessel of FIG. 7a including sail area.

FIG. 7d is a simplified drawing of the vessel shown in FIG. 7a , alsoshowing cross-section designations, A-A and B-B, for FIGS. 7e and 7 f.

FIG. 7e is a top view of the cross-section A-A of FIG. 7d , showing thecounter-leeward drift (CLD) hydrofoil with its flap 11 rotated towardleeward.

FIG. 7f is a top view of the cross-section B-B of FIG. 7d , showing thecounter-heeling (CH) hydrofoil with its flap 12 rotated toward windward.

FIG. 8a is an isometric view of another embodiment of the presentinvention showing counter-leeward drift and counter-heeling flaps on acanting keel sailing vessel.

FIG. 8b is a cross-sectional, stern view of the embodiment of thepresent invention depicted in FIG. 8a , with counter-leeward drift flap21 and counter-heeling flap 22 affixed to the keel which is shown inboth the canted and uncanted positions.

FIG. 9a is an isometric view of another embodiment of thecounter-leeward drift and counter-heeling members for of the presentinvention.

FIG. 9b illustrates the detail of the embodiment of the presentinvention shown in FIG. 9a showing both an upper, leading hydrofoilmember 101 and a lower, trailing hydrofoil member 102 hydrofoilprojecting from a common axis mounted within a keel.

FIG. 9c shows an isometric view of the embodiment of the combined heeland drift control assembly shown in FIG. 9b , detailing the constructionof the leading 101 and trailing 102 hydrofoil members incorporated on acommon axis.

FIG. 9d is a cross-sectional, stern view of the embodiment depicted inFIG. 9a shown on a 20 degree starboard tack.

FIG. 10 is a profile view illustrating yet another embodiment of thecounter-leeward drift 41 and counter-heeling 42 flaps of the presentinvention with non-vertical hinges.

FIG. 11a is a cross-sectional stern view, perpendicular to the coursesailed, PPCS, of still another embodiment of the present invention,depicting two vertically slidable hydrofoils 51 and 52.

FIG. 11b is a profile view illustrating one of the slidable hydrofoilsfrom the embodiment of FIG. 11a and an embodiment of the hydrofoil slidetrack or slot 58.

FIG. 11c is a cross-sectional stern view, perpendicular to the coursesailed, PPCS, of still another embodiment of the present invention,depicting two vertically slidable hydrofoils mounted on angled tracks.The tracks are in a plane essentially parallel to the midplane of thekeel through most of the lower portion of the keel, 57, but angle outfrom the midplane of the keel when they reach their uppermost positions.

FIG. 12a is a cross-sectional stern view, perpendicular to the coursesailed, PPCS, of another embodiment of the present invention, includingtwo vertically slidable, angled cross-section hydrofoils 61 and 62.

FIG. 12b is a cross-sectional stern view of an angled, opencross-section, sliding hydrofoil 71 embodiment, showing the detail nearthe hull of the sailing vessel.

FIG. 12c is a cross-sectional stern view of an angled sliding hydrofoil72 embodiment, showing the detail near the tip of the keel.

FIG. 13 is a chart comparing angle Beta β of FIG. 12 vs. EWf, CHf andCDf of the vessel depicted in FIG. 12 a.

FIG. 14a is a cross-sectional stern view of still another embodiment ofthe present invention, depicting a sailing vessel on a starboard tackhaving a port tack centerboard 87 retracted and a starboard tackcenterboard 97 shown rotated down into active position with an upper CLDhydrofoil 91 on the windward side and a lower CH hydrofoil 92 on theleeward side.

FIG. 14b is a cross-sectional stern view of still another embodiment ofthe present invention, depicting a sailing vessel on a starboard tackhaving a retracted port tack centerboard 126, angled counter-clockwiseby an amount p from the midplane 125 c of the hull, and a complimentarystarboard tack centerboard 127, angled clockwise by an amount p from themidplane 125 c of the hull and shown rotated down into active positionwith an upper CLD hydrofoil 128 on the windward side and a lower CHhydrofoil 129 on the leeward side.

FIG. 14c is a plan view of still another embodiment of the presentinvention, depicting a sailing vessel on starboard tack, having aretracted port tack centerboard 146, with the slot of its trunk 142rotated counter-clockwise to an angle ω from the design longitudinalaxis of the hull of the vessel and a complimentary starboard tackcenterboard 147 with the slot of its trunk 143 rotated clockwise to anangle ω from the design longitudinal axis of the hull of the vessel,said centerboard 147 shown rotated down into active position with anupper CLD hydrofoil 148 on the windward side and a lower CH hydrofoil149 on the leeward side.

FIG. 15a is a cross-sectional stern view of still another embodiment ofthe present invention, depicting a sailing vessel on a starboard tackhaving a port tack daggerboard 107 retracted and a starboard tackdaggerboard 117 shown inserted into active position with an upper CLDhydrofoil 111 on the windward side and a lower CH hydrofoil 112 on theleeward side.

FIG. 15b is a cross-sectional stern view of still another embodiment ofthe present invention, depicting a sailing vessel on a starboard tackhaving a retracted port tack daggerboard 136, with the slot of its trunk134 angled counter-clockwise by an amount tau τ from the midplane 135 cof the vessel, and a complimentary starboard tack daggerboard 137, withthe slot of its trunk 133 angled clockwise by an amount tau τ from themidplane 135 c of the vessel, said starboard daggerboard shown insertedinto active position with an upper CLD hydrofoil 138 on the windwardside and a lower CH hydrofoil 139 on the leeward side.

FIG. 15c is a plan view of still another embodiment of the presentinvention, depicting a sailing vessel on starboard tack, having aretracted port tack daggerboard 156, with the slot of its trunk 152disposed at an angle psi ψ counter-clockwise from the designlongitudinal axis of the hull of the vessel and a complimentarystarboard tack daggerboard 157, with the slot of its trunk 153 disposedat an angle psi ψ clockwise from the design longitudinal axis of thehull of the vessel; said starboard daggerboard 157 inserted down intothe active position with an upper CLD hydrofoil 158 on the windward sideand a lower CH hydrofoil 159 on the leeward side

FIG. 16a is a cross-sectional stern view of still another embodiment ofthe present invention, depicting a keel having a frame 164 with sides167 and 168 that can be deformed in the upper section, near the root, bya CLD cam 161 and in the lower section, near the tip, by a CH cam 162when the camshaft 163, which is controlled from above, is rotated.

FIG. 16b shows a top view, taken as section B-B designated in FIG. 16 a.

FIG. 16c shows a side or profile view, taken as section C-C designatedin FIG. 16 b.

FIG. 17 depicts a sailing vessel on a starboard tack having two CLDhydrofoils, active hydrofoil 171 and inactive hydrofoil 173, disposed atthe root end of keel 177 and two CH hydrofoils, active hydrofoil 174 andinactive hydrofoil 172, disposed at the tip end of keel 177.

FIG. 18 is a stern view of a sailing vessel on a starboard tack showingtwo rotatable hydrofoil members 185 and 186 mounted on axes one abovethe other in parallel disposition to each other and to the longitudinalaxis of the vessel. The upper member is shown with a cambered surfacedirected toward windward and the lower member is shown with a camberedsurface directed toward leeward.

BRIEF DESCRIPTION OF THE PREFERRED EMBODIMENTS

Turning now more particularly to the drawings, wherein like numbersrefer to like elements, characteristics of the present invention areshown in FIGS. 5-18, with particular emphasis on the twin hydrofoil keelmounted combination of a counter-leeward drift hydrofoil acting inconcert with a counter-heeling hydrofoil.

It is understood and defined as used herein that when a flap ishinge-mounted on the keel or similar appendage of a sailing vessel, theflap and the neighboring keel section act in conjunction with each otheras a hydrofoil. When the flap is rotated, the overall camber of thehydrofoil changes, thereby changing its hydrodynamic characteristics.Therefore, the forces that are cited herein, in connection with ahinged-flap, are to be considered as the forces that act on the flap aspart of the hydrofoil combination of the flap and related keel section.

The effectiveness of hydrofoils in the production of lift becomesapparent when we consider that the forces generated by airfoils as wellas hydrofoils are a product of four multipliers: the square of thevelocity, the area and lift coefficient of the foil and the density ofthe fluid, air or water, Recognizing the huge payloads that aircraft arecapable of lifting, primarily because of the velocity ingredient, wemust consider the great advantage that the hydrofoil has due to the factthat the density of water is about 850 times greater than air.

It is to be further understood that, as used herein:

-   -   The term “appendage” means a keel, a centerboard, a dagger        board, or a similar protrusion extending from the hull of a        sailing vessel and into the water.    -   The term “hull” means a vessel's shell or body, exclusive of        appendages, which provides buoyancy and structure upon which to        mount deck, cabin, sails, rigging, and the like. This term is        meant to include a monohull of conventional sailing vessels and        a single hull of the so-called multihull boats such as        catamarans and trimarans, where the multiple hulls are often        singularly referred to as pontoons.    -   The term “center of gravity” (CG) means the geometric center of        weight of the boat and every item in it.    -   The term “vertical center of gravity” (VCG) means the height at        which the center of gravity is located.    -   The term “center of buoyancy” (CB) means the center of gravity        of the water displaced by the boat.    -   The term “vertical center of buoyancy” (VCB) means the height at        which the center of buoyancy is located.    -   The term “waterline plane of the hull” means the two dimensional        area within a line defined by the intersection of the hull and        the surface of the water within which a vessel floats.    -   The “design waterline plane of the hull” means the plane within        which the designer intended the vessel to float at zero degrees        heel.    -   The “load waterline plane of the hull” means the plane within        which the completed vessel actually floats at zero degrees heel.        For purposes herein this will be considered to be the same as        the “design waterline plane of the hull”.    -   The “heeled or instant waterline plane” means the two        dimensional area within a line defined by the intersection of        the hull and the surface of the water when the vessel is heeling        at any given angle.    -   The term “design longitudinal axis of rotation, or rolling”        (DLAR) means a line extending fore and aft of the hull or        pontoon of a sailing vessel upon which the vessel initiates        rotation (or rolling) from an initial position of zero degrees        heeling. For purposes herein, this will be assumed to be close        to the waterline plane and bisect or be about halfway between        equal areas of the design waterline plane of the hull.    -   The term “instant longitudinal axis of rotation” (ILAR) means a        line extending fore and aft of the hull or pontoon of a sailing        vessel upon which the vessel rotates (or rolls) at any given        instant, position or heel angle. This is usually vertically        close to the waterline plane and horizontally located to enable        equal volumes of emergence and immersion on opposite sides of        the hull as the boat heels or rotates. The exact location        depends on various factors, but primarily the shape and weight        of the hull. For purposes herein, this axis will be assumed to        bisect or be about halfway between equal areas, to port and        starboard, of the heeled waterline plane of the hull. At the        position of zero degrees heeling, the ILAR is equal to the DLAR        and as the heeled waterline plane moves, relative to the hull        with increased heeling, the ILAR will move accordingly.    -   The term “midplane” means a bisecting, fore and aft, centered        plane of symmetry. The midplane of the hull, or hull midplane,        bisects the hull of a sailing vessel in the longitudinal        direction and is in a vertical attitude at a heeling angle of        zero degrees. Similarly, the midplane of an appendage, or        appendage midplane, bisects an appendage of a sailing vessel in        the longitudinal direction from the leading edge to the trailing        edge of the appendage. The plane of a conventional keel is        typically in the same plane as is the midplane of the hull.    -   An example of a midplane of a hull appears in FIG. 6e as        reference number 6. Also shown in this figure is an example of a        midplane of an appendage or keel, which appears as reference        number 16. It can be seen that in this case the two planes are        in alignment. Similarly, examples of appendage (e.g., keel,        centerboard, or dagger board) midplanes appear in FIGS. 6e, 14a        and 15a as reference numbers 16, 95 a and 115 a respectfully.

FIGS. 5 through 7 f depict a sailing vessel shown with hull or body 5,rudder 8S, keel 17, and ballast bulb 19. Specific attention is directedto two control flaps mounted on the keel, i.e., an upper,counter-leeward drift flap 11 and a lower, counter-heeling flap 12. Forthe sake of clarity, all of the drawings herein are not necessarily toscale and may be exaggerated to distinctly present the various elementsand angular locations.

FIG. 5 shows the hull 5 of a typical, but modified, according to thepresent invention, sailing yacht. Its keel 17 is rigidly attached at itsroot or base to the bottom of the hull 5, its midplane being in verticalalignment with the midplane of the hull. It also has a ballast bulb 19attached to its lower or tip end. The counter-leeward drift flap 11 isattached to the upper or root portion and trailing edge of the keel 17,close to the hull 5. The counter-heeling flap 12 is attached at thetrailing edge and at the lower end, or tip, of the keel 17, just abovethe ballast bulb 19. Although shown at the trailing edge of the keel,either or both of these hydrofoils or flaps, 11 and 12, can be attachedto the leading edge of the keel 17 where, similar to leading-edge flapson aircraft, they can perform the same function. The two aforementionedflaps, 11 and 12, are designed and located such that the center ofeffort of the counter-heeling flap 12 is at a considerably greaterdistance from the design longitudinal axis of rotation, or rolling,taken to be located at point R in FIG. 7a , of the vessel than is thecenter of effort of the counter leeward-drift flap 11. This distance isintended to provide a much longer moment arm for the counter heelingflap 12 than the moment arm of the counter leeward-drift flap 11. Thisallows the counter-heeling flap 12 to be much more effective in itsintended function. As the skilled artisan would readily appreciate, thedifferential of these moment arms can be increased or decreased as canbe the size, shape or locations of these foils to achieve the desiredresults.

FIGS. 6a, 6b, 6c, 6d and 6e more clearly show the elements of FIG. 5.Specifically, these figures show detailed views of the counter-leewarddrift flap 11 and the counter-heeling flap 12 shown in FIG. 5. The sizeand shape of the counter-leeward drift flap 11 and the counter-heelingflap 12 can be adapted to meet the objectives of any particular keeldesign. Additionally, in the embodiment shown in FIGS. 5, 6 a, 6 b, 6 c,6 d and 6 e, for each flap or hydrofoil, the angle of deflection can beindependently varied during sailing, to increase or decrease thehydrodynamic force exerted by the associated hydrofoil on the vessel asrequired in order to maximize sailing efficiency. For some designs, forexample to simplify or unify controls, the flaps may be coupled to actin accordance with a relationship designed into the coupling mechanism.Hinges 13 and 14 allow for flap movement. Control systems for varioushydrofoil movements are known in the art. The present inventionenvisages any such control system. Such systems could include mechanicaland/or electro-mechanical linkages powered by a crank, lever, hydraulicsystem, servomotor or the like.

Ideally, the CLD flap or hydrofoil will be located high on the keelappendage, as close to the root as efficiency will allow. This willposition its center of effective effort close to the design longitudinalaxis of rotation (FIGS. 6d and 6e , reference 10) which will minimizeits contribution to the heeling moments on the vessel. Complimentingthis concept, the CH flap or hydrofoil will be located as close to thelower or tip end of the keel or appendage as efficiency will allow. Thiswill position its center of effort at the maximum effective distancefrom the design longitudinal axis of rotation which will maximize itscontribution to the counter-heeling moments on the vessel. Reference ismade to FIG. 6e wherein the hinge 13 of CLD flap 11 and the hinge 14 ofCH flap 12 are shown to be located essentially within the midplane 16 ofthe keel or appendage. Now referring to FIG. 10 wherein the positioningof the hinges is further defined, the CLD flap is referenced as 41mounted on hinge 43 and the CH flap is referenced as 42 mounted on hinge44. While still located essentially within the midplane of the keel,hinges 43 and 44 are shown at respective angles δ₁ and δ₂ which areoriented at less than ninety (90) degrees, fore or aft, to a lateralplane (FIG. 6d , reference 15) perpendicular to the design longitudinalaxis of rotation of the vessel. Lateral plane 15 in FIG. 6d may also bedefined as the vertical plane that is perpendicular to the midplane 16of appendage or keel 17.

The complimentary function of the two hydrofoils or flaps willsimultaneously enable a net reduction in both the leeward drift and theheeling of virtually any sailing vessel so equipped. Sailing efficiencymay be thus easily maximized by the simple adjustment of the flap orhydrofoil controls.

FIG. 7a shows a stern view, in a plane perpendicular to the coursesailed (PPCS), of the sailing vessel, depicted in FIGS. 5 through 6 e,on a starboard tack, heeling at 20 degrees. Referring also to FIG. 7e ,in this attitude, the counter-leeward drift flap 11 is shown rotatedtoward the leeward side in order to generate a hydrodynamic force F_(LC)generally toward the windward side of the vessel. This force acts at thecenter of effort A of the CLD hydrofoil which is the combination of flap11 and its complementary section of keel 17. F_(LD) is the component ofthe hydrodynamic force F_(CLF) of the CLD hydrofoil, resolved into aplane perpendicular to the course sailed (PPCS). In turn, F_(LD) has ahorizontal component F_(CD) which is equal to F_(LD) Cos ϕ. (Refer toFIG. 7a ), where 4 is the heeling angle of the vessel. This is thecounter-leeward drift force contributed by the CLD hydrofoil.

Another component of force F_(LD) contributes to the heeling momentsacting on the vessel. This component, F_(H), also acts at the center ofeffort A of the CLD hydrofoil within a plane perpendicular to the coursesailed (PPCS). F_(H) is equal to F_(L) Cos θ, where θ is the anglebetween RA and the midplane of the keel. RA is the perpendiculardistance between the line of the force F_(H) and the instantlongitudinal axis of rotation, which is taken to be at point R in thefigure.

If the shape of a hull was perfectly cylindrical, that is, shaped like alog, the perfect symmetry of its circular cross-section would cause theaxis of rotation, or rolling, to reside at the intersection of themidplane and a projected line of the buoyancy force, regardless of theangle of heel. This would allow the vessel to immerse a volume on oneside of the vessel equal to the volume being emerged on the oppositeside of the vessel as the vessel rotates on this axis at any heelingangle. However, for other hulls, for example wine glass and ellipticalshaped cross-sections, the symmetry of the submerged cross-section islost upon heeling and, as the area of the instant waterline plane movesaway from the midplane with rotation of the hull, the instant axis ofrotation will move as well. The movement of the axis will closely followa position that continues to allow the area of the instant waterlineplane to be longitudinally bisected by this axis, thus assuring that thevolume of water displaced by immersion on one side of the axis isreplaced by an equal volume of water due to emergence on the oppositeside of the axis. The buoyant force necessary to support the weight ofthe vessel thus remains constant. It may also be noted that thevariation of cross-section along the length of the hull will also havean effect on the longitudinal trim of the vessel.

The component F_(H) multiplied by its perpendicular distance RA to theinstant longitudinal axis of rotation, R, is a heeling moment, F_(H)×RA,exerted by the CLD hydrofoil on the vessel.

The moment, F_(H)×RA, and the counter-leeward drift force, F_(LD) Cos ϕ,both of which are generated by the CLD hydrofoil when flap 11 isactuated, have counterparts that are generated by the CH hydrofoil whenflap 12 is actuated. These are treated as follows:

Referring to FIG. 7f the counter-heeling flap 12 is shown rotated towardthe windward side to generate a hydrodynamic force F_(CHF), directedgenerally toward the leeward side of the vessel. This force acts at thecenter of effort C of the CH hydrofoil which is the combination of flap12 and its complementary section of keel 17. F_(LH) is the component ofthe hydrodynamic force, F_(CHF) of the CH hydrofoil, resolved into aplane perpendicular to the course sailed (PPCS). Referring to FIG. 7a ,F_(LH), in turn, has a horizontal component F_(D), which is equal toF_(LH) Cos ϕ, where ϕ is the heeling angle of the vessel. F_(D) alsoacts at the center of effort C of the hydrofoil 12 in the planeperpendicular to the course sailed (PPCS). This is the leeward driftforce contributed by the CH hydrofoil.

The force F_(LH) also has a component, in the plane perpendicular to thecourse sailed that acts at the center of effort C of hydrofoil 12 in adirection perpendicular to the instant longitudinal axis of rotation Rof the vessel. This component, F_(CH), is equal to F_(LH) Cos μ, where μis the angle between RC and the midplane of the keel RC is theperpendicular distance between the line of force F_(CH), and the instantlongitudinal axis of rotation R of the vessel. The force F_(CH)multiplied by its perpendicular distance RC to the instant longitudinalaxis of rotation R of the vessel represents the counter-heeling moment,F_(CH)×RC, provided to the vessel by the CH hydrofoil.

An analysis of the effective weight forces, drift forces and heelingmoments more clearly shows how the efficiency of a sailing vessel can beimproved by this embodiment of the present invention.

The net change in effective weight force contributed to the vessel bythe CLD and CH hydrofoils when flaps 11 and 12 are activated (ΔEWF11/12), as depicted in FIG. 7a can be calculated as follows:ΔEWF 11/12=F _(LD) sine ϕ−F _(LH) sine ϕ  Eq. 1W-1:

where a negative value of ΔEWF 11/12 indicates an increase in effectiveweight

It can be seen that when F_(LD)=F_(LH), then: ΔEWF 11/12=0

As required, the net effective weight can easily be reduced by the helmor an associated automatic control system by rotating hydrofoil 11 anadditional amount toward leeward to increase F_(LD). As will be seenhereinafter, this will also increase the net counter-leeward drift forceand the net heeling moment on the vessel.

The drift forces contributed by the CLD and CH hydrofoils when flaps 11and 12 are activated, ΔLDF 11/12, can be summarized as follows:

Delta Leeward Drift Force (ΔLDF 11/12)=F_(CD)−F_(D)ΔLDF11/12=F _(LD) cosine ϕ−F _(LH) cosine ϕ  Eq. 1D-1:

-   Where: A positive value of ΔLDF 11/12 indicates an increase in    counter-drift forces.    -   F_(LD) is a component of the hydrodynamic force of the CLD foil,        of which flap 11 is an element, resolved into a plane        perpendicular to the course sailed, PPCS.    -   F_(LH) is a component of the hydrodynamic force of the CH foil,        of which flap 12 is an element, resolved into a plane        perpendicular to the course sailed, PPCS.    -   F_(CD) is the horizontal counter-leeward drift force component        of F_(LD), also acting in the plane perpendicular to the course        sailed, PPCS.    -   F_(D) is the horizontal leeward drift force component of F_(LH)        also acting in the plane perpendicular to the course sailed        (PPCS).    -   Phi (ϕ) is the heeling angle of the vessel.

The heeling moments contributed by the CLD and CH hydrofoils when flaps11 and 12 are activated, Δ CHM 11/12, can be summarized as follows:

Heeling Moment generated by the CLD hydrofoil when flap 11 is actuated(HM11):HM11=F _(H) ×RA=F _(LD) cosine θ×RA

-   -   Where:        -   R is the instant longitudinal axis of rotation of the            vessel.        -   A is the center of effort of the upper hydrofoil 11.        -   RA is the lever arm distance between points R and A.        -   Theta (θ) is the angle between RA and the midplane of the            keel 17.        -   F_(LD) is a component of the hydrodynamic force of the CLD            foil, of which flap 11 is an element, resolved into a plane            perpendicular to the course sailed, PPCS.        -   F_(H) is that component of force F_(LD) directed at right            angles to lever arm RA also acting in the plane            perpendicular to the course sailed (PPCS).            Counter-heeling moment generated by the CH hydrofoil when            flap 12 is actuated CHM 12:            CHM 12=F _(CH) ×RC=F _(LH) cosine μ×RC    -   Where:        -   R is the instant longitudinal axis of rotation of the vessel        -   C is the center of effort of the CH hydrofoil        -   RC is the lever arm distance between points R and C        -   Mu (μ) is the angle between RC and the midplane of the keel            17.        -   F_(LH) is a component of the hydrodynamic force of the CH            foil, of which flap 12 is an element, resolved into a plane            perpendicular to the course sailed (PPCS).        -   F_(CH) is that component of force F_(LH) directed at right            angles to lever arm RC, also acting in the plane            perpendicular to the course sailed (PPCS).            Delta (Δ) of the Counter-heeling Moments of CLD and CH when            flaps 11 and 12 are actuated (ΔCHM 11/12):            ΔCHM11/12=Counter-heeling Moment(CHM12)−Heeling Moment(HM11)            ΔCHM11/12=F _(CH) ×RC−F _(H) ×RA            ΔCHM11/12=F _(LH) cosine μ×RC−F _(LD) cosine θ×RA  Eq. 1H-1:    -   Where a positive value of ΔCHM 11/12 indicates a net increase in        counter-heeling moments

A further resolution of ΔCHM 11/12 can now be obtained as follows:Referring to FIG. 7b , which is a graphic representation of the anglesand dimensions of FIG. 7a , it can be seen that:cosine μ=DC/RCcosine θ=DA/RAThen:

$\begin{matrix}{{\Delta\;{CHM}\mspace{14mu} 11\text{/}12} = {{F_{LH}\mspace{14mu}{cosine}\mspace{14mu}\mu \times {RC}} - {F_{LD}\mspace{14mu}{cosine}\mspace{14mu}\theta \times {RA}}}} \\{= {{F_{LH} \times {DC}\text{/}{RC} \times {RC}} - {F_{LD} \times {DA}\text{/}{RA} \times {RA}}}}\end{matrix}$ $\begin{matrix}{{\Delta\;{CHM}\mspace{14mu} 11\text{/}12} = {{F_{LH} \times {DC}} - {F_{LD} \times {DA}}}} & {{{Eq}.\mspace{14mu} 1}H\text{-}2}\end{matrix}$

In addition to the above, the following relationship offers a convenientcomparison of the controlling counter-heeling moments generated by theCLD and CH hydrofoils when activated by rotation of flaps 11 and 12:

A Counter-heeling to Heeling Improvement Ratio (CHIR) contributed by thehydrofoils can be stated as:CHIR 12/11=Foil 12(CHM)/Foil 11(HM)CHIR 12/11=F _(LH) ×DC/F _(LD) ×DACHIR 12/11−F _(LH) /F _(LD) ×DC/DA  Eq. 1H-3:

It can be seen from the above relationship that a designer has a greatdeal of leverage in countering the heeling forces that act on a sailingvessel by dimensioning DC longer than DA. This embodiment of the presentinvention also affords the helm significant control of the heelingforces and drift forces, as conditions may dictate. By varying the angleof deflection of flaps 11 and 12, the forces F_(LH) and F_(LD) can bechanged to increase or decrease the heeling moment or drift force inresponse to the needs of the helm. It should be noted that, dependingupon the shape of the hull, the ratio of DC to DA will change to someextent as the vessel heels. For any design, the ratio can be determinedas soon as the shape of the hull is fixed. Equation 1H-3 also showsthat, if desired, in operation this deviation would be readily trimmedout with corrections to F_(LH) and/or F_(LD) made by the helm or by anassociated control system. Therefore, for simplification and explanatorypurposes herein, this ratio will be assumed to remain constant.

An example using typical parameters readily demonstrates the improvementin effective weight, drift and heeling characteristics made possible bythis embodiment of the present invention.

-   -   Given the vessel of FIG. 7a , heeling at an angle of 20 degrees,        designed with a ratio of DC to DA of 3:1 and making way to        windward with flaps 11 and 12 angled such that the CLD hydrofoil        generates two times the force of the CH hydrofoil:        The net change in effective weight force (ΔEWF11/12),        contributed by the hydrofoils, as depicted in FIG. 7a for this        example, can be calculated as follows:        ΔEWF 11/12=F _(LD) sine ϕ−F _(LH) sine ϕ  Eq.1W-1:    -   where a negative value of ΔEWF 11/12 indicates an increase in        effective weight        and given: F _(LD)=2F _(LH)        then: ΔEWF11/12=2F _(LH) sine ϕ−F _(LH) sine ϕ=F _(L) Hsine ϕ    -   Thus, for this example, there is a net reduction in effective        weight, equal to F_(LH) sine ϕ.

The drift forces contributed by the two hydrofoils in this example canbe obtained by a summarization of the horizontal forces.

Referring to Equation 1D-1 above, the net change in drift forces, ΔLDF11/12, can be determined as follows:

given:  F_(LD) = 2 × F_(LH) $\begin{matrix}{\begin{matrix}{{\Delta\;{LDF}\mspace{14mu} 11\text{/}12} = {{F_{LD}\mspace{14mu}{cosine}\mspace{14mu}\phi} - {F_{LH}\mspace{14mu}{cosine}\mspace{14mu}\phi}}} \\{= {{2\mspace{14mu} F_{LH}\mspace{14mu}{cosine}\mspace{14mu}\phi} - {F_{LH}\mspace{14mu}{cosine}\mspace{14mu}\phi}}}\end{matrix}{{{Therefore}\text{:}\mspace{14mu}\Delta\;{LDF}\mspace{14mu} 11\text{/}12} = {F_{LH}\mspace{14mu}{cosine}\mspace{14mu}\phi}}} & {{{Eq}.\mspace{14mu} 1}D\text{-}1}\end{matrix}$

Thus, for this example there is a net reduction in leeward drift forces,equal to F_(LH) cosine ϕ.

Reference is made to the fact that, unlike heeling, the drift forcesaffecting the vessel are not a function of moment arms.

Now referring to Equation 1 H-2 above, the counter-heeling improvementof foils 11 and 12, ΔCHM 11/12, can be determined as follows:ΔCHM11/12=F _(LH) ×DC−F _(LD) ×DA  From Eq. 1H-2:and given: DC=3×DAand: F _(LD)=2×F _(LH)Then: ΔCHM11/12=F _(LH) ×DC−2×F×DC/3ΔCHM11/12=1/3F _(LH) ×DCAgain, in this example, a positive value of ΔCHM 11/12 indicates a netreduction in heeling moments acting on a sailing vessel, equal to ⅓F_(LH)×DC.

The above example demonstrates that designs of the present invention, asexemplified by FIG. 7a , can produce a positive counter-leeward driftforce while simultaneously producing a positive counter-heeling momentand a net reduction in effective weight.

Further, the resultant counter-heeling moments generated by embodimentsof the present invention are able to work independently or inconjunction with counter-heeling moments produced by conventional, new,prior art and other designs including, but not limited to, such thatutilize ballast and/or moments produced by the weight of the vessel whenthe axis of rotation shifts due to heeling.

FIG. 7c shows a typical configuration wherein this embodiment of thepresent invention joins the ballast on a conventional sailing vessel. Toportray a simplified analysis of the heeling moments generated by theCLD and CH hydrofoils, in this figure only the forces that relate toheeling are shown and the instant longitudinal axis of rotation is shownto pass through point R. Again, the elements depicted in this figure arenot necessarily drawn to scale.

A summation of the moments (ΣM), when the vessel is in equilibrium, canthen be made as follows:ΣM=F _(SP) ×d _(S) +F _(K) ×d _(K) +F _(H) ×RA−F _(CH) ×RC−F _(W) ×d_(BW)=0  Eq. 1H-4:

Where:

F_(H) RA, F_(CH) and RC have been previously defined.

F_(SP) is a component of the aerodynamic force generated by the wind onthe sails resolved into a plane perpendicular to the course sailed,PPCS.

d_(S) is the perpendicular distance from the line of action of F_(SP)and the instant longitudinal axis of rotation R of the vessel.

F_(K) comprises the residual forces acting on the keel, includingrudder, hull and like forces but excluding the forces associated withthe CLD and CH hydrofoils which are shown separately.

d_(K) is the perpendicular distance from the line of action of F_(K) andthe instant longitudinal axis of rotation R of the vessel.

F_(W) is the weight, including ballast 19, of the vessel assumed to beconcentrated at the center of gravity (G) of the vessel.

d_(BW) is the perpendicular distance between the lines of action of theweight

-   -   force F_(W) and the buoyancy force F_(B).

F_(B) is the buoyancy force acting on the vessel, equal and opposite toF_(W).

When added, as shown in FIG. 7c , to a conventional ballasted sailingvessel, this embodiment of the present invention will assist thecounter-heeling capabilities of the vessel, such that the vessel willheel less and/or ballast weight can be reduced with a significantimprovement in the sailing efficiency of the vessel.

It also can be seen from FIG. 7c that the dimensions d_(BW) is equal tozero when the vessel is not heeling. Therefore, the CLD and CHhydrofoils, flaps, or members of the present invention can provide aresultant counter-heeling moment, even when the vessel is sailing erect.This enables the ideal possibility of tacking a sailing vessel towindward, with heeling moments acting but being counter-acted withoutheeling the sailing vessel,

The design criteria for this invention, including moment arms,hydrofoils, flaps, or members, shapes and sizes, mounting arrangements,control systems and the like can be varied in many combinations at thediscretion of designers to simultaneously and significantly improve theheeling and the drift characteristics of sailing vessels. Also, controlsfor these embodiments, provided for the helmsman, will permit immediateadjustments as demand requires during their operation. By increasing ordecreasing the angle of rotation of either the CLD or CH flap, thehelmsman can vary the lift force generated by either or both hydrofoilsto suit the immediate conditions.

A general description of the operation of the embodiments of the presentinvention, as depicted in FIG. 7a where the two flaps or hydrofoils areboth trailing and rotatable follows. In all cases, the upper hydrofoilis the counter-leeward drift hydrofoil and the lower hydrofoil is thecounter-heeling hydrofoil. The former performs its named function bybeing rotated toward leeward to generate a hydrodynamic force towardwindward; this force acts primarily to counter leeward drift forces. Atthe same time, the latter performs its named function by being rotatedtoward the windward side of the vessel to generate a hydrodynamic forcetoward leeward; this force acts primarily to counter heeling moments onthe sailing vessel. In these embodiments, each of the flaps can berotated independently to provide more or less lift. Also, at thedesigner's discretion, the flaps can be coupled by design to rotateaccording to a prescribed algorithm. The algorithm can include inputsfrom the helm, apparent wind speed and wind direction, heeling angle,position (GPS), heading, drift, track, weather, destination and otherrelative factors, as desired.

Most important, the twin hydrofoil, keel of the present invention can beused by sailing vessels of virtually every design category. For example,FIGS. 8a and 8b show a sailing vessel as described above but with acanting keel 27, rather than a fixed keel. In this case, counter-leewarddrift flap 21 and counter-heeling flap 22, similar to previouslydescribed flaps 11 and 12, are mounted on the canting keel 27. As shownin FIG. 5a , both of these flaps are mounted on the keel, reducing orprecluding a requirement for additional separate appendages or devicesto counter leeward drift forces or heeling moments.

As another example where this embodiment of the present invention isenvisaged to be applied, refer to the vessel depicted in FIG. 4 of thisapplication. In such case, a CLD flap can be mounted on the upperportion of the keel 2 and a CH flap can be mounted on the lower portionof the keel 2, either above or below the fins 5 a and 5 b. The forcesgenerated by the CLD and CH flaps would function to complement theaction of fins 5 a and 5 b.

America's Cup Class (ACC) Rule, Version 5.0, Rule 17.10 states that “Themaximum number of movable appendages shall be two.” Also, Rule 17.10 (a)states that “movement (of appendages) is limited to rotation only.” Inorder to qualify under these rules, a sailing vessel configured with arudder can only have one additional rotating appendage. The embodimentof the present invention shown in FIGS. 9a, 9b, 9c and 9d , is intendedprovide benefits of the present invention and to qualify a sailingvessel for America's Cup Class Rule. Like the designs shown in FIGS. 5through 8 b, the embodiment shown in FIGS. 9a through 9d simultaneouslyprovides both counter-leeward drift forces and counter-heeling moments.As depicted in FIGS. 9a through 9d , only two rotating appendages areutilized on the vessel, a rudder 8 and the assembly 100. Like the wingedkeel of FIG. 4, with two wings or hydrofoils, configured together as asingle unit, assembly 100 is also a single unit configured with twohydrofoils that enable both counter-leeward drift forces and counterheeling moments to be generated.

FIG. 9a shows a sailing vessel similar in design to the sailing vesselof FIGS. 5 through 7, previously described; however, the counter-leewarddrift hydrofoil member 101 and the counter-heeling hydrofoil member 102are each an integral part of a composite assembly 100 and, in operation,are designed to rotate as a single unit. As seen in FIGS. 9a and 9b ,the counter-leeward drift foil 101 is shown projecting from axel 103toward the leading edge of the keel 37 rather than toward the trailingedge of the keel. Also, the counter heeling foil 102 is shown extendingfrom axel 103 toward the trailing edge of the keel 37. FIG. 9b shows adetailed view of the assembly 100 installed in the keel 37 and rotatedin a counter-clockwise direction when viewed from above. In thisembodiment, the upper and forward section, 101, of assembly 100 isshaped like and is intended to function, in concert with its neighboringsection of keel 37, like a hydrofoil. Since it is located near the topof the assembly, its primary function is intended to providecounter-leeward drift forces. The lower and trailing section 102 ofassembly 100 is also shaped like and is intended to function, in concertwith its neighboring section of the keel 37, as a hydrofoil. Since it islocated near the lower extremity of the keel, its primary function isintended to provide counter heeling moments: If a designer wishes, hecan project the upper foil toward the trailing edge and the lowerhydrofoil toward the leading edge; they will still move toward oppositesides of the keel when assembly 100 is rotated and this will not changetheir function. Again, the upper foil is always the Counter-leewardDrift foil and the lower foil is always the Counter-heeling hydrofoil.

The components of assembly 100, depicted in FIGS. 9b and 9c , compriseits axel 103 and two hydrofoil members 101 and 102. The assembly 100 ismounted in an upper bearing 104, affixed to the canoe body 5, orproximate to the upper end of the keel 37 and a lower bearing 105mounted proximate to the lower end of the keel 37 or on the uppersurface of the ballast bulb 39. Positioned near the upper end of theaxel is a counter-leeward drift hydrofoil member 101, which extendstoward the leading edge of the keel 37. Positioned near the lower end ofthe axel is a counter-heeling hydrofoil member 102, which extends towardthe trailing edge of the keel 37. The configuration is such that, as theassembly 100 rotates, the hydrofoil members 101 and 102 move to oppositesides of the keel FIG. 9d shows a partial schematic, aft view of thevessel heeling at 20 degrees on a starboard tack. In this case, whenAssembly 100 rotates counterclockwise, as viewed from above, the upperand forward, counter-leeward drift flap 101 rotates toward the leewardside of keel 37, generating a lift toward the windward side of the keel37. At the same time, the lower and trailing, counter-heeling flap 102,which also extends from axel (shaft) 103 but to the trailing edge of thekeel 37, rotates to the windward side of the keel 37, generating lifttoward the leeward side of the keel 37. These two flaps, 101 and 102,are intended to function similarly to the flaps 11, 12, 21 and 22 ofFIGS. 5 through 8 b, such that their locations on a keel, or similarappendage, positions the lower CH flap at a significantly greaterdistance from the design longitudinal axis of rotation of the vesselthan the upper CLD flap is positioned from the design longitudinal axisof rotation, thus enabling a sailing vessel to counter both leewarddrift forces and heeling moments simultaneously. It should be noted herethat the two hydrofoils, 101 and 102, do not have to be sized and shapedsuch that they each provide the same amount of lift. Rather, the liftcharacteristics can be varied or modified according to the objectives ofthe sailing vessel designer. In addition, because of this unique design,only one rotating member, Assembly 100, is utilized to create bothcounter-leeward drift forces and counter-heeling moments. Thissimplifies the controls and enables designs of high performance sailingvessels that incorporate a rudder and a counter-leewarddrift/counter-heeling appendage, exemplified by this embodiment of thepresent invention, to qualify under ACC Version 5.0, Rules 17.10 and17.10(a).

FIG. 10 shows a keel appendage 47, which has two flap-type hydrofoils,41 and 42, mounted on hinges 43 and 44 respectively. This is similar tokeel appendage 17 of FIGS. 6a-6b with hydrofoils 11 and 12 mounted onhinges 13 and 14. The significant difference between these twoappendages is in the angles of the hinges on each keel 17 or 47 thatconnect the flaps to the keel. It can be seen in FIGS. 6a, 6b, 6c, 6dand 6e that the axes of the mounting hinges 13 and 14 are essentiallywithin the midplane of the keel and are positioned vertically or, inthis case, reasonably parallel to a plane perpendicular to the designlongitudinal axis of rotation (reference 15 in FIG. 6d ). As shown inFIG. 10, however, the axis of hinges 43 and 44 are raked back from thevertical at an angle, Delta 1 (δ₁) and Delta 2 (δ₂), respectively. If afoil is so mounted, when it is rotated out of the plane of the keel, toeither side, as opposed to a foil with a vertical hinge, which generateslift essentially normal to the plane of the keel, it will direct itshydrodynamic force not just out from the plane of the keel, but out andup, such that an upward force component will be generated. Therefore,the utilization of this concept enables the vessel designer to build inan increased amount of upward force for reduced effective weight whenthe hydrofoils are rotated. The more that the angles 56 and 62 are rakedback from the vertical the greater that upward component will be. Thiscomponent will be at the expense of the net counter-leeward drift andcounter-heeling forces, but it enables the vessel designer to modify orbalance these forces to achieve his desired sailing characteristic. Itfollows that the opposite effect can be achieved in either or both flapsby angling the hinge(s) on either or both flaps in the oppositedirection, that is, a forward rake from the vertical. In this case, theforce of the hydrofoil will be directed in a more downward direction.This will increase the effective weight force and benefit both thecounter-leeward drift characteristics and the counter-heeling moments.The present invention envisages designs that may utilize either thesame, different or variable values for the angles δ₁ and δ₂ and eithermay be in a forward or aft raked direction.

Ideally, the CLD flap or hydrofoil will be located high on the keelappendage, as close to the root as efficiency will allow. This willposition its center of effective effort close to the design longitudinalaxis of rotation (FIGS. 6d and 6e , reference 10) which will minimizeits contribution to the heeling moments on the vessel. Complimentingthis concept, the CH flap or hydrofoil will be located as close to thelower or tip end of the keel or appendage as efficiency will allow. Thiswill position its center of effort at the maximum effective distancefrom the design longitudinal axis of rotation which will maximize itscontribution to the counter-heeling moments on the vessel. Reference ismade to FIG. 6d wherein the hinge 13 of CLD flap 11 and the hinge 14 ofCH flap 12 are shown to be located essentially within the midplane (FIG.6e , reference 16) of the keel or appendage. Now, again referring toFIG. 10, wherein the positioning of the hinges is further defined, theCLD flap is referenced as 41 mounted on hinge 43 and the CH flap isreferenced as 42 mounted on hinge 44. While still located essentiallywithin the midplane of the keel, hinges 43 and 44 are shown atrespective angles 6S and 62 which are oriented at less than ninety (90)degrees, fore or aft, to a lateral plane (FIG. 6d , reference 15)perpendicular to the design longitudinal axis of rotation of the vessel.Lateral plane 15 in FIG. 6d may also be defined as the vertical planethat is perpendicular to the midplane 16 of appendage or keel 17.

It should be noted that the present invention also envisages embodimentswhere (1) the flaps have hinges with fixed alignments and (2) the flapshave hinges where the alignment of the hinges is adjustable.

Another embodiment of the present invention is shown in FIG. 11a . FIG.11a shows a stern view, in a plane perpendicular to the course sailed,of a sailing vessel heeling at 20 degrees on a starboard tack; that isthe starboard side of the vessel is to windward. Attached to the keel 57are two hydrofoils that are made as mirror images of each other, astarboard-side hydrofoil 51 and a port-side hydrofoil 52. As seen inFIG. 11b , the keel includes tracks 58, one on each side of the keel.These tracks may run (i) parallel to the keel leading edge, as shown(ii) parallel to the keel trailing edge or (iii) along any othersubstantially vertical line. The tracks permit the hydrofoils to beslid, by suitable means, to the top position on the keel 57 or to thebottom position on the keel 57, as desired by the helm. It is intendedthat that the hydrofoil on the leeward side be positioned at the lowestpoint on the keel with its cambered surface and thus its hydrodynamicforce being directed generally in a leeward direction and the hydrofoilon the windward side be positioned at the highest point on the keel withits cambered surface and thus its hydrodynamic force being directedgenerally in a windward direction. When the tack of the vessel isreversed, the positions of the hydrofoils will also be reversed. Whenrunning before the wind they can be positioned opposite to each other atany convenient position on the keel.

In order to generate the maximum counter-heeling moment on the sailingvessel, the hydrofoil 52 on the leeward side of the keel 57 is moved tothe bottom position near the tip of the keel, as shown in FIG. 11a ,where it will generate a hydrodynamic force generally toward the leewardside of the sailing vessel. A component of that leeward force, resolvedinto a vertical plane, perpendicular to the course sailed (PPCS), isshown as lift force F_(LH). In turn, F_(LH) has a component F_(CH), alsoacting in the plane perpendicular to the course sailed, that is equal toF_(LH) Cos μ that contributes to the counter-heeling moments acting onthe vessel F_(CH) acts at the point of effective effort C in a directionperpendicular to the lever arm RC. Lever arm RC is the distance betweenthe point of effective effort, C, and the instant longitudinal axis ofrotation, taken to be at point R of the vessel. Angle μ is the angleincluded within RC and the midplane of the keel 57. Since F_(CH) acts atright angles to RC, it exerts a counter-heeling moment of F_(CH)×RC orF_(LH) Cos μ×RC. At the same time, F_(D) the horizontal component ofF_(LH), adds to the leeward drift forces acting on the sailing vessel.F_(D) is equal to F_(LH) Cos ϕ, where ϕ is the heeling angle.

Concurrently, on the windward side of the keel 57, the hydrofoil 51 ismoved to the top position near the root of the keel, as shown in FIG.11a , where it will generate a hydrodynamic force, generally toward thewindward side of the sailing vessel. A component of that windward force,resolved into a vertical plane, perpendicular to the course sailed(PPCS), is shown as lift force F_(LD). In turn, F_(LD) has a horizontalcomponent F_(CD) which acts at the center of effort A and is equal toF_(LD) Cos ϕ, also acting in a plane perpendicular to the course sailed(PPCS), and is the resulting counter-leeward drift force F_(CD) exertedby CLD hydrofoil 51. This horizontal component, F_(CD), will counterleeward drift forces acting on the vessel.

Another component of force F_(LD) contributes to the heeling momentsacting on the vessel. This force component, F_(H) also acting in a planeperpendicular to the course sailed (PPCS), is equal to F_(LD) Cos θ andacts at the center of effort A in a direction perpendicular to the leverarm RA. Lever arm RA is the distance from the center of effort A to theinstant longitudinal axis of rotation R of the vessel. Angle θ is theangle included between RA and the midplane of the keel 57. Since F_(H)acts at right angles to RA, it exerts a heeling moment of F_(H)×RA orF_(LD) Cos θ×RA.

Referring to FIG. 11a , an analysis of the downward or effective weightforces, drift forces and heeling moments discussed above more clearlyshows how the efficiency of a sailing vessel can be improved by thisembodiment of the present invention.

The net change in effective weight force contributed by hydrofoils 51and 52 (ΔEWF 51/52) of the vessel as depicted in FIG. 11a can becalculated as follows:ΔEWF 51/52=F _(LD) sine ϕ−F _(LH) sine ϕ  Eq, 2W-1:

-   -   where a negative value of ΔEWF 51/52 indicates an increase in        effective weight.

Since hydrofoils 51 and 52 are intended to be mirror images of eachother, for purposes of this example, without considering leeward drift,it can be assumed that F_(LD)=F_(LH).then: ΔEWF 51/52=0

While essentially no increase in effective weight force is incurred bythis embodiment of the present invention, it is evident that asignificant decrease in effective weight is obtained by a reduction ofthe heeling angle, provided by this embodiment of the present invention,which proportionally reduces the downward component of the wind forceexerted by the sails on the vessel. On a sailing vessel not so equipped,it is necessary to direct the vessel at a greater leeward angle tocounter the downward component of the wind force on the sails. Thishowever, points the vessel at an increased angle from the course sailedand increases the drag on the vessel.

A summation of the drift forces contributed by hydrofoils, 51 and 52, asshown in FIG. 11a is as follows:

Delta Leeward Drift Force of foils 51 and 52 (ΔLDF 51/52):ΔLDF 51/52=F _(CD) −F _(D)ΔLDF 51/52=F _(LD) cosine ϕ−F _(LH) cosine ϕ  Eq. 21D-1:

-   Where: A positive value of ΔLDF 51/52 indicates a net increase in    counter-leeward drift forces.    -   F_(LD) is a lift component of the hydrodynamic force of foil 51,        resolved into a plane perpendicular to the course sailed, PPCS.    -   F_(LH) is a lift component of the hydrodynamic force of foil 52,        resolved into a plane perpendicular to the course sailed, PPCS.    -   F_(CD) is the horizontal counter-leeward drift force component        of F_(LD), also acting in the plane perpendicular to the course        sailed, PPCS.    -   F_(D) is the horizontal leeward drift force component of F_(LH)        also acting in the plane perpendicular to the course sailed,        PPCS.    -   Phi (ϕ) is the heeling angle of the vessel.        and given: F _(LD) =F _(LH)        then: ΔLDF51/52=F _(LH) cosine ϕ−F _(LH) cosine ϕ˜=0

Thus, the leeward drift force that is added by the lower hydrofoil 52 iscancelled by the counter-leeward drift force generated by the upperhydrofoil 51.

A summation of the heeling moments contributed by hydrofoils, 51 and 52,is as follows:

Heeling Moment of Hydrofoil 51 (HM 51):HM51=F _(H) ×RA=F _(LD) cosine θ×RAWhere:

-   -   R is the instant longitudinal axis of rotation of the vessel    -   A is the center of effort of the upper hydrofoil 51.    -   RA is the lever arm distance between points A and R.    -   Theta (θ) is the angle between RA and the midplane of the keel        57.    -   F_(LD) is a lift component of the hydrodynamic force of foil 51,        resolved into a plane perpendicular to the course sailed (PPSC).    -   F_(H) is that component of force F_(LD) directed at right angles        to lever arm RA also acting in the plane perpendicular to the        course sailed (PPSC).        The counter-heeling moment generated by hydrofoil 52 is:        Counter-heeling Moment of Hydrofoil 52 (CHM 52):        CHM 52=F _(CH) ×RC=F _(LH) cosine μ×RC

Where: R is the instant longitudinal axis of rotation of the vessel

-   -   C is the center of effort of the lower hydrofoil 52    -   RC is the lever arm distance between points R and C    -   Mu (μ) is the angle between BC and the midplane of the keel 57.    -   F_(LH) is a lift component of the hydrodynamic force of foil 52,        resolved into a plane perpendicular to the course sailed (PPSC).    -   F_(CH) is that component of force F_(LH) directed at right        angles to lever arm RC also acting in the plane perpendicular to        the course sailed (PPSC).        Delta (Δ) of the Counter-heeling Moments of Foils 51 and 52        (ΔCHM 51/52):        ΔCHM 51/52=CHM 52−HM 51        ΔCHM51/52=F _(CH) ×RC−F _(H) ×RA        ΔCHM 51/52=F _(LH) cosine μ×RC−F _(LD) cosine θ×RA  Eq.2H-1:    -   Where a positive value of ΔCHM 51/52 indicates a net increase in        counter-heeling moments

A further resolution can now be obtained as follows:

Referring to FIG. 7b , which is a graphic representation of the anglesand dimensions of FIGS. 7a, and 11a , it can be seen that:cosine μ=DC/RCcosine θ=DA/RAand since:ΔCHM 51/52=F _(LH) cosine μ×RC−F _(LD) cosine θ×RAΔCHM 51/52=F _(LH) ×DC/RC×RC−F _(LD) ×DA/RA×RAΔCHM 51/52=F _(LH) ×DC−F _(LD) ×DA  Eq. 2H-2:and given: F _(LH) =F _(LD)ΔCHM 51/52=F _(LH)(DC−DA)

It is well to note here that by increasing the ratio of DC to DA, adesigner will be able to increase the counter heeling moments withoutaffecting leeward drift or effective weight forces and also have theflexibility to compensate for any difference anticipated between F_(LH)and F_(LD) caused by sailing at a leeward angle.

In addition to the above, the following relationship offers a convenientcomparison of the controlling counter-heeling factors offered by foils52 and 51: A Counter-heeling to Heeling Improvement Ratio (CHIR 52/51)contributed by foils 52 and 51 can be stated as:CHIR 52/51=Foil 52(CHM)/Foil 51(HM)CHIR 52/51=F _(LH) ×DC/F _(LD) ×DACHIR 52/51=F _(LH) /F _(LD) ×DC/DA  Eq. 2H-3:and given: F _(LH) =F _(LD)CHIR 52/51=DC/DA

As discussed earlier, prior art designs that are intended to counterheeling moments, do so, but at the expense of adding leeward driftforces. The embodiment of this invention shown in FIG. 11a creates acounter-heeling moment without an increase in leeward drift forces. Asshown above, it can be seen that by designing the two hydrofoils asmirror images of each other, the horizontal components of their liftingforces are equal but opposite and therefore the additive drift force ofthe lower, counter heeling foil is cancelled by the opposing drift forceof the upper, counter-leeward drift foil; also, since the hydrodynamicforces of the two hydrofoils are equal and the lever arm of the lower,counter-heeling hydrofoil is greater than the lever arm of the uppercounter-leeward drift hydrofoil, there will be a positive netcounter-heeling moment improvement produced by these two hydrofoilsequal to the ratio of DC to DA.

FIG. 11c , which is a stern view, in a plane perpendicular to the coursesailed (PPCS), depicts a variation in the lateral direction of thetracks of hydrofoils 51 and 52 which are shown here as 51′ and 52′respectively.

In this variation the two tracks of hydrofoils 51′ and 52′ are in planesessentially vertical and parallel to the midplane of the keel 57′ formost of their travel in the lower portion of the keel, 57′, but angleaway from the midplane of the keel 57′ when they reach their uppermostpositions where they function as CLD hydrofoils. This variation isintended to park each hydrofoil, when it is in the uppermost position,with its cambered surface facing somewhat down from parallel to theplane of the keel. This will then direct the hydrodynamic force of theupper, counter-leeward drift foil down, to a degree equal to the angleof β′ from a direction perpendicular to the midplane of the keel 57′. Itcan be seen by analyzing the force vectors of the upper hydrofoil thatsuch a modification will not only increase the counter-leeward driftforce when the vessel is heeling but will also reduce the heeling momentcontributed by that foil.

Such an analysis will show a benefit to hydrofoil 51′ and/or 52′, whenlocated in the uppermost CLD position, comparable to the benefit thatthe angle β contributes to hydrofoil 61 and/or 62 respectively depictedin FIG. 12 and analyzed hereinafter.

Although the results obtained from utilizing the embodiment of thepresent invention described in FIG. 11a will satisfy a great many designobjectives, a modification of that embodiment will permit designers tovary the relative effect that these hydrofoils have on each of theinterrelated characteristics of counter-leeward drift force,counter-heeling moment and effective weight. Such a modificationaccomplishes this by changing the direction of the forces generated atthe surfaces of the hydrofoils. This is depicted in FIG. 12a , and ispresented below.

An analysis treated hereinafter relating to FIG. 12a depicts slidinghydrofoils which are fashioned with their cambered surfaces positionedat an angle β to the midplane of the keel. It will be shown, for examplein FIG. 13, that the counter-heeling, counter-leeward drift andeffective weight characteristics can be modified to significantlyimprove the efficiency of a sailing vessel by changing the angle β. Itis also apparent that designs of the embodiment depicted in FIG. 10 mayutilize different values for each of angles δ₁ and δ₂ depending upon theobjectives. However, if both of these angles were made comparable to theangle β of FIG. 12a , the results would be analogous.

FIG. 12a shows a stern view perpendicular to the course sailed of asailing vessel heeling at 20 degrees on a starboard tack Attached to thekeel 67 are two hydrofoils that are made as mirror images of each other,a starboard-side hydrofoil 61 and a port-side hydrofoil 62. Essentially,these hydrofoils are designed, mounted and function similar to thehydrofoils shown in FIG. 11a but with one significant distinction.Referring to FIG. 11a , it can be seen that the cambered surface of eachhydrofoil, 51 and 52 is parallel to the midplane of the keel, whereasFIG. 12a shows that the plane of the cambered surface of the starboardside hydrofoil 61 is fixed at an angle β rotated clockwise from themidplane of the keel and the cambered surface of the port side hydrofoil62 is fixed at an equal angle β rotated counter-clockwise from themidplane of the keel. This positioning, or angling, changes thedirection of the forces generated by the hydrofoils relative to thedegree that they are angled. It will be seen from the following analysisthat a change in the direction of these forces can have a broad effecton the resultant heeling moments, leeward drift forces, and downwardacting forces that affect the efficiency of a sailing vessel. Thus, byselecting an appropriate angle β, a designer will be able to change therelationship between these characteristics to obtain results that areclosest to his design objectives.

An analysis of the effect that the angle β, shown in FIG. 12a , willhave on the resultant downward force or effective weight,counter-leeward drift, and counter-heeling moment characteristicsproduced by the hydrofoils will demonstrate the interrelationshipbetween these parameters. To simplify the following analysis and sincethe leeward angle sailed is minimized by the counter-leeward driftforces of the present invention, any effect that the leeward angle hason the hydrodynamic forces is not considered. Further, the analysisreveals how designers may favor specific functions by angling thehydrofoils to increase the efficiency of a sailing vessel or advancecertain design objectives.

The net change in effective weight force contributed by hydrofoils 61and 62 (ΔEWF 61/62) of the vessel as depicted in FIG. 12a can becalculated as follows:ΔEWF 61/62=F _(LD) sine(ϕ−β)−F _(LH) sine(ϕ+β)  Eq. 3W-1:

-   Where: a negative value of ΔEWF 61/62 indicates an increase in    effective weight    -   F_(LD) is a lift component of the force of the windward        hydrofoil 61 resolved into a plane that is perpendicular to the        course sailed (PPCS).    -   F_(LH) is a lift component of the force of the leeward hydrofoil        62 resolved into a vertical plane that is perpendicular to the        course sailed (PPCS).    -   Phi (ϕ) is the heeling angle of the vessel.    -   Beta (β) is the angle that the cambered surface of either        hydrofoil is rotated away from the midplane of the keel. As        viewed from the stern,    -   the cambered surface of the starboard side hydrofoil 61 is        rotated clockwise from the midplane of the keel and the cambered        surface of the port side hydrofoil 62 is rotated        counter-clockwise from the midplane of the keel.        and given: F _(LD) =F _(LH)        then: ΔEWF 61/62=F _(LH)[sine (ϕ−β)−sine (ϕ+β)]    -   For convenience in graphically representing the characteristic        of    -   ΔEWF 61/62, the term [sine (ϕ−β)−sine (ϕ+β)] can be called the        effective weight factor (EWf 61/62).    -   Then, as will also be presented in FIG. 13:        EWf 61/62=[sine(ϕ−β)−sine(ϕ+β)]

When a vessel is heeling on a starboard tack, as shown in FIG. 12a , thecontributions to the drift forces contributed by hydrofoils 61 and 62are determined as follows:

Delta Leeward Drift Force of foils 61 and 62 (ΔLDF 61/62):ΔLDF61/62=F _(CD) −F _(D)ΔLDF61/62=F _(LD) cosine(ϕ−β)−F _(LH) cosine(ϕ+β)  Eq.3D-1:

-   -   Where: A positive value of ΔLDF 61/62 indicates a net increase        in counter-drift forces.        -   F_(LD) is a lift component of the force of the windward            hydrofoil 61 resolved into a plane that is perpendicular to            the course sailed (PPCS).        -   F_(LH) is a lift component of the force of the leeward            hydrofoil 62 resolved into a plane that is perpendicular to            the course sailed (PPCS).        -   F_(CD) is the horizontal counter-leeward drift force            component of F_(LD), also acting in the plane perpendicular            to the course sailed.        -   F_(D) is the horizontal leeward drift force component of            F_(LH), also acting in the plane perpendicular to the course            sailed.        -   Phi (ϕ) is the heeling angle of the vessel        -   Beta (β) is the angle that cambered surface of either            hydrofoil is rotated away from the midplane of the keel. As            viewed from the stern, the cambered surface of the starboard            side hydrofoil 61 is rotated clockwise from the midplane of            the keel and the cambered surface of the port side hydrofoil            62 is rotated counter-clockwise from the midplane of the            keel.    -   and since, by design: F_(LD)=F_(LH)        ΔLDF 61/62=F _(LH)[cosine(ϕ−β)−cosine(ϕ+β)]  Eq.3D-2:        For convenience in analysis, the quantity [cosine (ϕ−β)−cosine        (ϕ+β)] can be defined as the “Counter Leeward-drift factor”        (CDf) and is further described below.

Thus, the net drift or counter-drift forces contributed by the twohydrofoils, 61 or 62, is a product of that component of the force of onehydrofoil, resolved into the plane perpendicular to the course sailed,times the Counter Leeward-drift factor, CDf FIG. 13 shows how CDf variesrelative to a change in p.

A summation of the heeling moments contributed by hydrofoils 61 and 62shown in FIG. 12a can be calculated as follows:

The heeling moment generated by hydrofoil 61 is:

Heeling Moment of Hydrofoil 61 (HM 61):HM 61=F _(H) ×RA=F _(LD) cosine(θ+β)×RA

Where:

-   -   R is the location of the instant longitudinal axis of rotation        of the vessel.    -   A is the center of effort of the upper hydrofoil 61.    -   RA is the distance between points R and A.    -   Theta (θ) is the angle between RA and the midplane of the keel        67.    -   Beta (β) is the angle that the cambered surface of hydrofoil 61        is rotated clockwise away from the midplane of the keel.    -   F_(LD) is the lift component of the force of the windward        hydrofoil 61 resolved into a plane that is perpendicular to the        course sailed (PPCS).    -   F_(H) is that component of lift force F_(LD) that acts at right        angles to lever arm RA also acting in the plane perpendicular to        the course sailed (PPCS).        F _(LD) =F _(LH)        The counter-heeling moment generated by hydrofoil 62 is:        Counter-heeling Moment of Hydrofoil 62 (CHM 62):        CHM 62=F _(CH) ×RC=F _(LH) cosine(μ−β)×RC    -   Where:        -   R is the location of the instant longitudinal axis of            rotation of the vessel.        -   C is the center of effort of the lower hydrofoil 62.        -   RC is the distance between points R and C.        -   Beta (β) is the angle that the cambered surface of hydrofoil            62 is rotated counter-clockwise away from the midplane of            the keel 67.        -   Mu (μ) is the angle between RC and the midplane of the keel            57.        -   F_(LH) is the lift component of the force of the leeward            hydrofoil 62 resolved into a plane that is perpendicular to            the course sailed (PPCS).        -   F_(CH) is that component of lift force F_(LH) that acts at            right angles to lever arm RC also acting in the plane            perpendicular to the course sailed (PPCS).            F _(LD) =F _(LH)

-   The change in Counter-Heeling Moment provided by hydrofoils 61 and    62 (ΔCHM 61/62) is:

$\begin{matrix}{{\Delta\;{CHM}\mspace{14mu} 61\text{/}62} = {{{CHM}\mspace{14mu} 62} - {{HM}\mspace{14mu} 61}}} \\{= {{F_{CH} \times {RC}} - {F_{H} \times {RA}}}}\end{matrix}$ΔCHM 61/62=[F _(LH) cosine(μ−β)×RC]−[F _(LD) cosine(θ+β)×RA]  Eq. 3H-1:

Where a positive value of ΔCHM 61/62 indicates a net increase incounter-heeling forces.

Given that the two hydrofoils, 61 and 62, are designed to generateessentially equal forces, making F_(LH)=F_(LD).

then:ΔCHM 61/62=[F _(LH) cosine(μ−β)×RC]−[F _(LH) cosine(θ+β)×RA]

The following example shows how this relationship can be reducedfurther:

Given the sailing vessel of FIG. 12a which is shown heeling at an angleof 20 degrees and has the two hydrofoils positioned at design locationssuch that lever arm RC is two times as long as lever arm RA. That is,for this example, RA=RC/2.

Then

$\begin{matrix}{{\Delta\;{CHM}\mspace{14mu} 61\text{/}62} = {\left\lbrack {F_{LH}\mspace{14mu}{cosine}\mspace{14mu}\left( {\mu - \beta} \right) \times {RC}} \right\rbrack - \left\lbrack {F_{LH}\mspace{14mu}{cosine}\mspace{14mu}\left( {\theta + \beta} \right) \times {RC}\text{/}2} \right\rbrack}} \\{= {F_{LH} \times {RC} \times \left\lbrack {{\cos\left( {\mu - \beta} \right)} - {1\text{/}2\mspace{14mu}{cosine}\mspace{14mu}\left( {\theta + \beta} \right)}} \right\rbrack}}\end{matrix}$For purposes of this example, wherein RC=2 RA, the quantity [cosine(μ−β)−½ cosine (ϕ+β)] can be defined as the “Counter Heeling factor2/1”, (CHf 2:1). This will hold for any design of this embodiment of thepresent invention where RC=2 RA.

Thus, when RC=2 RA, the net heeling moment contributed by the twohydrofoils, 61 and 62, is a product of the component of the force of onehydrofoil resolved into the plane perpendicular to the course sailed,F_(LH), times the lever arm RC of the lower hydrofoil times the CounterHeeling factor, CHf 2:1. FIG. 13 shows how CHf 2:1 of the vesseldescribed in FIG. 12a varies relative to an angular change β in theorientation of the surfaces of the hydrofoils. Also, to simplify theanalysis for the purposes herein, an estimation of the approximatevalues of μ and θ for the vessel shown in FIG. 12a can be made at equals12 degrees and θ equals 33 degrees.

Although many sailing vessel designs would take advantage of thebenefits and the simplicity of hydrofoils 61 and 62 with relatively lowangles of beta, designs that incorporate larger angles could be madewith an open hydrofoil profile by utilizing a configuration similar tothat shown in FIGS. 12b and 12c . This would serve to reduce the dragthat might be introduced by hydrofoils with a high beta angle and of aclosed profile design.

FIG. 12b shows a sliding, open-hydrofoil design. This open-hydrofoildesign presents a slimmer profile to the incident fluid flow to reducedrag. The figure shows the upper portion of keel 77 on a starboard tack,the starboard hydrofoil 71 positioned at the upper position on keel 77,the cambered surface 73 of starboard hydrofoil 71, the keyed, slidablefoot 75 of starboard hydrofoil 71 and the lift force F_(LD) of starboardfoil 71.

FIG. 12c shows the lower portion of keel 77 on a starboard tack, theport side hydrofoil 72 positioned at the lower position on keel 77, thecambered surface 74 of port side hydrofoil 72, the keyed, slidable foot76 of port side hydrofoil 72 and the lift force F_(LH) of port side foil72.

Referring now to FIG. 13, the effect of redirecting the hydrodynamicforces generated by hydrofoils 61 and 62 or 71 and 72 of FIGS. 12a to12c is shown. The graph shows EWf, CDf and CHf plotted against values ofthe angle beta, β. A wide range of values is offered to allow designersto make comparisons and weigh alternatives. Ultimately, specific valuesof beta (β) will be chosen to obtain performance characteristics in tunewith design objectives.

FIG. 13 shows the relationship between the Effective Weight factor, EWfthe Counter Drift factor, CDf and the Counter Heeling factor, CHf andhow they vary with a change in the angle beta (β). By definition, whenβ=0, the surfaces of the hydrofoils are parallel to the midplane of thekeel and then the values of EWf CDf and CHf and are the same as thevalues for FIG. 11a . The addition of the angle β provides designerswith the ability to vary the interrelationships of effective weight,counter-drift and counter-heeling characteristics to optimizeperformance of sailing vessels according to their design objectives. Asshown, values of β above 0 degrees will add effective weight andincrease both counter-leeward drift forces and counter-heeling moments.A reduction in the effective weight could also be achieved by theselection of an angle β less than 0 degrees but this will reduce thecounter-leeward drift forces and counter-heeling moments.

It is important to note that underlying the benefits portrayed in thecurves as shown, is the fact that an improvement in one of thesecharacteristics generally benefits one or more of the othercharacteristics. For example, a reduction in the heeling angle willaccordingly reduce the downward force component of the sails, yielding asignificant reduction in the effective weight of the sailing vessel.Accompanying this, the reduction in the downward force componenttranslates into an increase in the forward driving force component onthe vessel.

It becomes apparent that embodiments of the present invention can beapplied to various appendages that extend from a sailing vessel hull,including fixed appendages such as conventional keels and winged keelsand appendages affixed movably such as canting keels and rudders and thelike. Also, specifically included are removable appendages such ascenterboards and daggerboards

Such an application is shown in the schematic diagram FIG. 14a , whichis a stern view of a sailing vessel on a starboard tack. This figuredepicts two centerboards 87 and 97 mounted side-by-side, within a trunk83, on an axel 84 such that each centerboard can be pivoted downwardinto the active position when desired. Centerboard 97 is shown in theactive position for a starboard tack. As configured, it has a CLDhydrofoil 91 mounted on its uppermost portion which will generate aforce generally in the windward direction of the vessel. It also has aCH hydrofoil 92 mounted on its lowermost portion which will generate aforce generally in the leeward direction of the vessel. In thisstarboard tack mode, centerboard 87, with CLD hydrofoil 81 and CHhydrofoil 82 attached, is shown retracted to the inactive position.Although centerboard 87 is shown mounted on the port side of the vesseland centerboard 97 on the starboard side, these positions could bereversed depending upon the objectives of the designer.

FIG. 15a , which is a schematic diagram of a stern view of a sailingvessel on a starboard tack, depicts two daggerboards 107 and 117 mountedside-by-side, within a trunk 113, having two slide slots 106, such thateach daggerboard can be inserted and slid downward into the activeposition when desired. Daggerboard 117 is shown in the active positionfor a starboard tack. As configured, it has a CLD hydrofoil 111 mountedon its uppermost portion which will generate a force generally in thewindward direction of the vessel. It also has a CH hydrofoil 112 mountedon its lowermost portion which will generate a force generally in theleeward direction of the vessel. In this starboard tack mode,daggerboard 107, with CLD hydrofoil 109 and CH hydrofoil 110 attached,is shown retracted to the inactive position. Although daggerboard 107 isshown mounted on the port side of the vessel and daggerboard 117 on thestarboard side, these positions could be reversed depending upon theobjectives of the designer.

Embodiments are also envisaged as shown in FIG. 14b , which is a sternview of a sailing vessel on a starboard tack, wherein the single axel 84of FIG. 14a described above is replaced by two axels, a starboard axel120 and a port axel 121. In this embodiment each axel would be disposedat an angle rho (p) from the horizontal or design waterline plane of thehull, such that, when the appropriate centerboard is rotated down to itsactive position when the vessel is heeling during a tack, it would bedirected in a more vertical direction and penetrate more deeply into thewater. For example, during a starboard tack of a vessel, as shown inFIG. 14b , the starboard centerboard 127 would be rotated on its axel120 downwardly into the active position and, as shown, would bepositioned in a more vertical attitude by an amount equal to the angleρ. On a port tack, the port centerboard 126, mounted on its port axel121, which is rotated by an amount p in the opposite direction from thehorizontal or design waterline plane of the hull, would also bepositioned in a more vertical attitude by an amount equal to the angleρ. This would direct the forces generated by the hydrofoils in a morehorizontal direction and sink the centerboards deeper into the water.Also envisaged are such axels with axes that are adjustable, permittingan increase or decrease in the value of angle ρ.

Embodiments are also envisaged as shown in FIG. 15b , which is a sternview of a sailing vessel on a starboard tack, wherein the parallel slots106 of FIG. 15a described above are replaced by two slots, a starboardslot within trunk 133 and a port slot within trunk 134.

In this embodiment each slot would be disposed at an angle tau (t) fromthe vertical axis of the vessel, such that, when the appropriatedaggerboard is inserted downwardly into its active position when thevessel is heeling during a tack, it would be directed at a more verticalangle and would penetrate more deeply into the water. For example,during a starboard tack of a vessel, as shown in FIG. 15b , thestarboard daggerboard 137 would be inserted downwardly into the slot oftrunk 133, which is angled clockwise from the vertical midplane of thevessel. It would then reside in its active station and, as shown, wouldbe positioned in a more vertical attitude by an amount equal to theangle τ. On a port tack, the port daggerboard 136, would be inserteddownwardly into the slot of trunk 134, which is angled counter-clockwisefrom the vertical midplane of the vessel. It would then reside in itsactive station and be positioned in a more vertical attitude by anamount equal to the angle r. This would direct the forces generated bythe hydrofoils in a more horizontal direction and sink the daggerboardsdeeper into the water. Also envisaged are such trunks with slots thatare adjustable, permitting an increase or decrease in the value of angler at the discretion of the helm.

Referring now to FIG. 14c which is a plan view showing a sailing vesselwith starboard centerboard 147 rotated down to the active position for astarboard tack and port centerboard 146 shown retracted to the inactiveposition. Centerboards 147 and 146 are mounted on axels 140 and 141respectively that are affixed perpendicular to the sides of trunks 143and 142, each side of which is configured, as shown, at an angle omega(ω) from the design longitudinal axis of the vessel. On each tack of thevessel, the orientation of the centerboard at an angle ω to the designlongitudinal axis of the vessel will increase the angle of attackrelative to the incident fluid flow of the appropriate centerboard,enabling it to generate additional counter-leeward drift forces whilepermitting the hull of the vessel to point more directly toward theincident fluid flow or course sailed. Also envisaged are such axels withaxes that are adjustable, permitting the value of angle ω to beincreased or decreased at the discretion of the helm.

FIG. 15c is a plan view of a sailing vessel having two slots, each ofwhich provide for a daggerboard to be inserted and slid downward intoits active position on the appropriate tack. On a starboard tack, astarboard daggerboard 157, with CLD hydrofoil 158 and CH hydrofoil 159,is inserted down to the active position and port daggerboard 156, withCLD hydrofoil 155 and CH hydrofoil 154, is retracted to the inactiveposition. This is reversed for a port tack. Daggerboards 157 and 156 areconfigured to slide within slots that are defined by parallel innersurfaces of the trunks 153 and 152 respectively, said surfaces beingdirected, as shown, at an angle psi (y) to the longitudinal axis of thevessel. On each tack of the vessel, the orientation of the centerboardat the angle ψ to the longitudinal axis of the vessel will increase theangle of attack of the appropriate centerboard enabling it to generateadditional counter-leeward drift forces while permitting the hull of thevessel to point more directly toward the incident fluid flow or coursesailed. Also envisaged are such trunks or slots that are adjustable,permitting the value of angle ψ to be increased or decreased at thediscretion of the helm.

In yet other single daggerboard or single centerboard embodiments, thehydrofoils could be fixed and symmetrical front to back when viewed fromthe top and the daggerboard or centerboard and its holding mechanismdesigned such that, when the tack of the vessel is reversed, thedaggerboard or centerboard can be easily be withdrawn from its activeposition, reversed and reinserted for the new tack. Combinations ofthese fixed and adjustable hydrofoil embodiments are also envisaged.

In embodiments having adjustable hydrofoils or flaps, the skilledartisan could readily incorporate known control mechanisms for thedaggerboard or centerboard. Further, known interface mechanisms could beplaced in an accessible location on a portion of the daggerboard orcenterboard exposed to the helmsman, or at some other location insidethe vessel and connected to the daggerboard or centerboard by knownlinkages control systems or circuits

As will be appreciated by the skilled artisan, other embodiments of thesliding hydrofoil design described above could be made wherein thehydrofoils have any other fixed hydrodynamic shape. The presentinvention envisages embodiments where both hydrofoils are easilyremovable and replaceable, to account for breakage or in order toquickly adapt performance to different sailing conditions.

Further, the shape of hydrofoils utilized in the present invention couldbe adjustable or modifiable in any manner such as through inflation ordeformation of entire surfaces or portions of each hydrofoil, throughthe use of materials capable of being deformed by air or hydraulicpressure, levers, cams, servomotors, or the like or by adjustable,interconnected rigid sections capable of changing the surface of thehydrofoil.

Such an embodiment is depicted in schematic diagram FIG. 16a showing asailing vessel on a starboard tack. FIG. 16b shows a top view, taken assection B-B designated in FIG. 16a . FIG. 16c shows a side view, takenas section C-C designated in FIG. 16b . The figures show a keel assemblycomprising a frame 164 affixed to hull 5, bearings 165 and 166 affixedto the hull 5 and the tip end of frame 164 respectively, a rotatableshaft 163 mounted in said bearings 165 and 166, a deformable firstsurface 167 affixed to frame 164 on the starboard side of the keelassembly, a deformable second surface 168 affixed to frame 164 on theport side of the keel assembly, an upper CLD cam 161 locked to shaft 163and a lower CH cam 162 locked to shaft 163. As shown, the shaft has beenrotated to activate the keel assembly for a starboard tack. In thismode, the upper CLD cam pushes against the upper portion of firstsurface 167 giving the upper section of surface 167 a camber. At thesame time, the lower CH cam pushes against the lower portion of secondsurface 168 giving the lower section of second surface 168 a camber.Thus, the upper portion of surface 167, acting as a CLD hydrofoilgenerates a force generally in the windward direction of the vesselwhile the lower section of surface 168 acts as CH hydrofoil generating aforce generally in the leeward direction of the vessel. When the tack isreversed to a port tack, the shaft will be rotated 180 degrees togenerally reverse the CLD and CH forces. The shapes of the cams could besuch and the degree of rotation controllable to permit adjustableshaping of the deformable surfaces in order to vary their liftcharacteristics as desired.

Other adjustable hydrofoil embodiments would be particularly useful inapplications where hydrofoils are disposed on opposite sides of thekeel, but are not slidable. In such embodiments, two or more adjustablehydrofoils would be attached to each side of the keel. By way of themechanisms described above, these hydrofoils could lay flat against thekeel until operated. When operated, the appropriate hydrofoils wouldexpand or deform to create the counter heeling or counter-leeward driftforces as needed.

Such an application is shown in the schematic diagram FIG. 17 which is astern view, in a plane perpendicular to the course sailed, of a sailingvessel on a starboard tack. This figure depicts a keel 177 attached tothe hull 5 of the vessel at its root end and having a ballast bulb 179attached to its tip end. Also attached proximate to the root end of keel177 are two inflatable CLD hydrofoils. Since the vessel is shown on astarboard tack, the starboard side CLD hydrofoil 171 is shown inflatedto generate a hydrodynamic force F_(LD) generally in the windwarddirection and the port side CLD hydrofoil 173 is shown deflated, asshown. On a port tack, starboard side CLD hydrofoil 171 would bedeflated and port side CLD hydrofoil 173 would be inflated to generate ahydrodynamic force generally toward the new windward direction.Proximate to the tip end of keel 177 are two inflatable CH hydrofoils.When the vessel is on a starboard tack as shown, the port side CHhydrofoil 174 would be inflated to generate a hydrodynamic force F_(LH)generally in the leeward direction and the starboard side CH hydrofoil172 would be deflated, as shown. On a port tack, the port side CHhydrofoil 174 would be deflated and the starboard side CH hydrofoil 172would be inflated to generate a hydrodynamic force generally toward thenew leeward direction. Thus on either tack, counter-leeward drift (CLD)forces and counter-heeling (CH) forces would be generatedsimultaneously.

Another embodiment of the present invention is shown in FIG. 18 whereintwo rotatable hydrofoils 185 and 186 are mounted on an appendage, suchas a keel 187 of a sailing vessel, one above the other on axes 181 and182, each parallel to the chord of the appendage and each havingcambered surfaces 188 and 189, respectively, on one side and lessercambered surfaces 183 and 184, respectively, on the opposite side. Whentacking, the upper member, disposed toward the root of the appendage andacting as a CLD hydrofoil 185, would be rotated such that its morecambered surface 188 would be facing toward the windward side of thevessel to generate a hydrodynamic force toward windward, while the lowermember, disposed toward the tip end of the appendage and acting as a CHhydrofoil 186, would be rotated such that its more cambered surface 189would be facing toward leeward to generate a hydrodynamic force towardleeward. The amount of inflation of these hydrofoils could be adjustableto allow control of their individual hydrodynamic shapes.

For sailing vessels generally, the most preferred embodiment is thatshown in FIGS. 5-7 f and described above.

For sailing vessels following the design strictures of the America's Cupthe most preferred embodiment is that shown in FIGS. 9a-9d and describedabove. Such an embodiment, incorporated on a sailing vessel also havinga rudder or other single rotatable appendage would qualify for TheAmerica's Cup Class Rule, Version 5.0, dated 15 Dec. 2003, Section D,Rules 17.10 and 17.10 (a).

Finally, as the skilled artisan will readily appreciate, although theembodiments disclosed herein describe the present invention, many otherimprovements will also occur and should be understood to be within thespirit and scope of this invention, which is only to be limited by thefollowing claims:
 1. A keel for use in a sailing vessel comprising: akeel having a leading edge and a trailing edge; a keel tip area disposednear the end of the keel that is farthest away from said sailing vessel;a keel root area disposed near the portion of the keel that is closestto said sailing vessel; a first track disposed on a first side of saidkeel, adapted to receive a first slideable hydrofoil member; a secondtrack disposed on a second side of said keel, adapted to receive asecond slideable hydrofoil member; wherein said slidable members areeach capable of sliding from said keel root area to said keel tip area.2. The keel of claim 1 wherein said keel is a canting keel.
 3. The keelof claim 1 wherein said keel is removable from said sailing vessel. 4.The keel of claim 1 or claim 2 wherein said first track and said secondtrack are disposed substantially parallel to said leading edge.
 5. Akeel for use in a sailing vessel comprising: a keel having a leadingedge and a trailing edge; a keel tip area disposed near the end of thekeel that is farthest away from said sailing vessel; a keel root areadisposed near the portion of the keel that is closest to said sailingvessel; a first track disposed on a first side of said keel, adapted toreceive a first slideable member; a second track disposed on a secondside of said keel, adapted to receive a second slideable member; whereinsaid slidable members are each capable of sliding from said keel rootarea to said keel tip area; wherein said first track and said secondtrack are disposed substantially parallel to said leading edge.
 6. Akeel for use in a sailing vessel comprising: a canting keel having aleading edge and a trailing edge; a keel tip area disposed near the endof the keel that is farthest away from said sailing vessel; a keel rootarea disposed near the portion of the keel that is closest to saidsailing vessel; a first track disposed on a first side of said keel,adapted to receive a first slideable member; a second track disposed ona second side of said keel, adapted to receive a second hydrofoilmember; wherein said slidable members are each capable of sliding fromsaid keel root area to said keel tip area; wherein said first track andsaid second track are disposed substantially parallel to said leadingedge.
 7. A keel for use in a sailing vessel comprising: a removable keelhaving a leading edge and a trailing edge; a keel tip area disposed nearthe end of the keel that is farthest away from said sailing vessel; akeel root area disposed near the portion of the keel that is closest tosaid sailing vessel; a first track disposed on a first side of saidkeel, adapted to receive a first slideable member; a second trackdisposed on a second side of said keel, adapted to receive a secondslideable member; wherein said slidable members are each capable ofsliding from said keel root area to said keel tip area; wherein saidfirst track and said second track are disposed substantially parallel tosaid leading edge.
 8. A keel for use in a sailing vessel comprising: acanting keel having a leading edge and a trailing edge; a keel tip areadisposed near the end of the keel that is farthest away from saidsailing vessel; a keel root area disposed near the portion of the keelthat is closest to said sailing vessel; a first track disposed on afirst side of said keel, adapted to receive a first slideable member; asecond track disposed on a second side of said keel, adapted to receivea second hydrofoil member; wherein said slidable members are eachcapable of sliding from said keel root area to said keel tip area. 9.The keel of claim 8 wherein said slideable members are hydrofoils. 10.The keel of claim 9 wherein said first track and said second track aredisposed substantially parallel to said leading edge.